FPF ring theory: faithful modules and generators of mod-R
This is the first book on the subject of FPF rings and the systematic use of the notion of the generator of the category mod-R of all right R-modules and its relationship to faithful modules. This carries out the program, explicit of inherent, in the work of G Azumaya, H. Bass, R. Dedekind, S. Endo,...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1984
|
| Schriftenreihe: | London Mathematical Society lecture note series
88 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | This is the first book on the subject of FPF rings and the systematic use of the notion of the generator of the category mod-R of all right R-modules and its relationship to faithful modules. This carries out the program, explicit of inherent, in the work of G Azumaya, H. Bass, R. Dedekind, S. Endo, I. Kaplansky, K. Morita, T. Nakayama, R. Thrall, and more recently, W. Brandal, R. Pierce, T. Shores, R. and S. Wiegand and P. Vamos, among others. FPF rings include quasi-Frobenius rings (and thus finite rings over fields), pseudo-Frobenius (PF) rings (and thus injective cogenerator rings), bounded Dedekind prime rings and the following commutative rings; self-injective rings, Prufer rings, all rings over which every finitely generated module decomposes into a direct sum of cyclic modules (=FGC rings), and hence almost maximal valuation rings. Any product (finite or infinite) of commutative or self-basic PFP rings is FPF. A number of important classes of FPF rings are completely characterised including semiprime Neotherian, semiperfect Neotherian, perfect nonsingular prime, regular and self-injective rings. Finite group rings over PF or commutative injective rings are FPF. This work is the culmination of a decade of research and writing by the authors and includes all known theorems on the subject of noncommutative FPF rings. This book will be of interest to professional mathematicians, especially those with an interest in noncommutative ring theory and module theory |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 31 May 2016) |
| Beschreibung: | 1 online resource (1 volume (various pagings)) |
| ISBN: | 9780511721250 |
| DOI: | 10.1017/CBO9780511721250 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043940477 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s1984 |||| o||u| ||||||eng d | ||
| 020 | |a 9780511721250 |c Online |9 978-0-511-72125-0 | ||
| 024 | 7 | |a 10.1017/CBO9780511721250 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511721250 | ||
| 035 | |a (OCoLC)967695616 | ||
| 035 | |a (DE-599)BVBBV043940477 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 512/.4 |2 19eng | |
| 084 | |a SI 320 |0 (DE-625)143123: |2 rvk | ||
| 084 | |a SK 230 |0 (DE-625)143225: |2 rvk | ||
| 100 | 1 | |a Faith, Carl |d 1927-2014 |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a FPF ring theory |b faithful modules and generators of mod-R |c Carl Faith, Stanley Page |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1984 | |
| 300 | |a 1 online resource (1 volume (various pagings)) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a London Mathematical Society lecture note series |v 88 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 31 May 2016) | ||
| 520 | |a This is the first book on the subject of FPF rings and the systematic use of the notion of the generator of the category mod-R of all right R-modules and its relationship to faithful modules. This carries out the program, explicit of inherent, in the work of G Azumaya, H. Bass, R. Dedekind, S. Endo, I. Kaplansky, K. Morita, T. Nakayama, R. Thrall, and more recently, W. Brandal, R. Pierce, T. Shores, R. and S. Wiegand and P. Vamos, among others. FPF rings include quasi-Frobenius rings (and thus finite rings over fields), pseudo-Frobenius (PF) rings (and thus injective cogenerator rings), bounded Dedekind prime rings and the following commutative rings; self-injective rings, Prufer rings, all rings over which every finitely generated module decomposes into a direct sum of cyclic modules (=FGC rings), and hence almost maximal valuation rings. Any product (finite or infinite) of commutative or self-basic PFP rings is FPF. A number of important classes of FPF rings are completely characterised including semiprime Neotherian, semiperfect Neotherian, perfect nonsingular prime, regular and self-injective rings. Finite group rings over PF or commutative injective rings are FPF. This work is the culmination of a decade of research and writing by the authors and includes all known theorems on the subject of noncommutative FPF rings. This book will be of interest to professional mathematicians, especially those with an interest in noncommutative ring theory and module theory | ||
| 650 | 4 | |a FPF rings | |
| 650 | 4 | |a Associative rings | |
| 650 | 4 | |a Modules (Algebra) | |
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 0 | 7 | |a Quasi-Frobenius-Ring |0 (DE-588)4176637-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ringtheorie |0 (DE-588)4126571-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a FPF-Ring |0 (DE-588)4155116-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a FPF-Ring |0 (DE-588)4155116-3 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Ringtheorie |0 (DE-588)4126571-3 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 689 | 2 | 0 | |a Quasi-Frobenius-Ring |0 (DE-588)4176637-4 |D s |
| 689 | 2 | |8 3\p |5 DE-604 | |
| 700 | 1 | |a Page, Stanley |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-27738-9 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511721250 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029349447 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511721250 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511721250 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176881022402560 |
|---|---|
| any_adam_object | |
| author | Faith, Carl 1927-2014 |
| author_facet | Faith, Carl 1927-2014 |
| author_role | aut |
| author_sort | Faith, Carl 1927-2014 |
| author_variant | c f cf |
| building | Verbundindex |
| bvnumber | BV043940477 |
| classification_rvk | SI 320 SK 230 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9780511721250 (OCoLC)967695616 (DE-599)BVBBV043940477 |
| dewey-full | 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511721250 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03962nmm a2200613zcb4500</leader><controlfield tag="001">BV043940477</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s1984 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511721250</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-72125-0</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511721250</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511721250</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)967695616</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043940477</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.4</subfield><subfield code="2">19eng</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 320</subfield><subfield code="0">(DE-625)143123:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 230</subfield><subfield code="0">(DE-625)143225:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Faith, Carl</subfield><subfield code="d">1927-2014</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">FPF ring theory</subfield><subfield code="b">faithful modules and generators of mod-R</subfield><subfield code="c">Carl Faith, Stanley Page</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">1984</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (1 volume (various pagings))</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">London Mathematical Society lecture note series</subfield><subfield code="v">88</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 31 May 2016)</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This is the first book on the subject of FPF rings and the systematic use of the notion of the generator of the category mod-R of all right R-modules and its relationship to faithful modules. This carries out the program, explicit of inherent, in the work of G Azumaya, H. Bass, R. Dedekind, S. Endo, I. Kaplansky, K. Morita, T. Nakayama, R. Thrall, and more recently, W. Brandal, R. Pierce, T. Shores, R. and S. Wiegand and P. Vamos, among others. FPF rings include quasi-Frobenius rings (and thus finite rings over fields), pseudo-Frobenius (PF) rings (and thus injective cogenerator rings), bounded Dedekind prime rings and the following commutative rings; self-injective rings, Prufer rings, all rings over which every finitely generated module decomposes into a direct sum of cyclic modules (=FGC rings), and hence almost maximal valuation rings. Any product (finite or infinite) of commutative or self-basic PFP rings is FPF. A number of important classes of FPF rings are completely characterised including semiprime Neotherian, semiperfect Neotherian, perfect nonsingular prime, regular and self-injective rings. Finite group rings over PF or commutative injective rings are FPF. This work is the culmination of a decade of research and writing by the authors and includes all known theorems on the subject of noncommutative FPF rings. This book will be of interest to professional mathematicians, especially those with an interest in noncommutative ring theory and module theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">FPF rings</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Associative rings</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Modules (Algebra)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Categories (Mathematics)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quasi-Frobenius-Ring</subfield><subfield code="0">(DE-588)4176637-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ringtheorie</subfield><subfield code="0">(DE-588)4126571-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">FPF-Ring</subfield><subfield code="0">(DE-588)4155116-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">FPF-Ring</subfield><subfield code="0">(DE-588)4155116-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Ringtheorie</subfield><subfield code="0">(DE-588)4126571-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Quasi-Frobenius-Ring</subfield><subfield code="0">(DE-588)4176637-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Page, Stanley</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-27738-9</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511721250</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029349447</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511721250</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511721250</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043940477 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:13Z |
| institution | BVB |
| isbn | 9780511721250 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349447 |
| oclc_num | 967695616 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (1 volume (various pagings)) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Faith, Carl 1927-2014 Verfasser aut FPF ring theory faithful modules and generators of mod-R Carl Faith, Stanley Page Cambridge Cambridge University Press 1984 1 online resource (1 volume (various pagings)) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 88 Title from publisher's bibliographic system (viewed on 31 May 2016) This is the first book on the subject of FPF rings and the systematic use of the notion of the generator of the category mod-R of all right R-modules and its relationship to faithful modules. This carries out the program, explicit of inherent, in the work of G Azumaya, H. Bass, R. Dedekind, S. Endo, I. Kaplansky, K. Morita, T. Nakayama, R. Thrall, and more recently, W. Brandal, R. Pierce, T. Shores, R. and S. Wiegand and P. Vamos, among others. FPF rings include quasi-Frobenius rings (and thus finite rings over fields), pseudo-Frobenius (PF) rings (and thus injective cogenerator rings), bounded Dedekind prime rings and the following commutative rings; self-injective rings, Prufer rings, all rings over which every finitely generated module decomposes into a direct sum of cyclic modules (=FGC rings), and hence almost maximal valuation rings. Any product (finite or infinite) of commutative or self-basic PFP rings is FPF. A number of important classes of FPF rings are completely characterised including semiprime Neotherian, semiperfect Neotherian, perfect nonsingular prime, regular and self-injective rings. Finite group rings over PF or commutative injective rings are FPF. This work is the culmination of a decade of research and writing by the authors and includes all known theorems on the subject of noncommutative FPF rings. This book will be of interest to professional mathematicians, especially those with an interest in noncommutative ring theory and module theory FPF rings Associative rings Modules (Algebra) Categories (Mathematics) Quasi-Frobenius-Ring (DE-588)4176637-4 gnd rswk-swf Ringtheorie (DE-588)4126571-3 gnd rswk-swf FPF-Ring (DE-588)4155116-3 gnd rswk-swf FPF-Ring (DE-588)4155116-3 s 1\p DE-604 Ringtheorie (DE-588)4126571-3 s 2\p DE-604 Quasi-Frobenius-Ring (DE-588)4176637-4 s 3\p DE-604 Page, Stanley Sonstige oth Erscheint auch als Druckausgabe 978-0-521-27738-9 https://doi.org/10.1017/CBO9780511721250 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Faith, Carl 1927-2014 FPF ring theory faithful modules and generators of mod-R FPF rings Associative rings Modules (Algebra) Categories (Mathematics) Quasi-Frobenius-Ring (DE-588)4176637-4 gnd Ringtheorie (DE-588)4126571-3 gnd FPF-Ring (DE-588)4155116-3 gnd |
| subject_GND | (DE-588)4176637-4 (DE-588)4126571-3 (DE-588)4155116-3 |
| title | FPF ring theory faithful modules and generators of mod-R |
| title_auth | FPF ring theory faithful modules and generators of mod-R |
| title_exact_search | FPF ring theory faithful modules and generators of mod-R |
| title_full | FPF ring theory faithful modules and generators of mod-R Carl Faith, Stanley Page |
| title_fullStr | FPF ring theory faithful modules and generators of mod-R Carl Faith, Stanley Page |
| title_full_unstemmed | FPF ring theory faithful modules and generators of mod-R Carl Faith, Stanley Page |
| title_short | FPF ring theory |
| title_sort | fpf ring theory faithful modules and generators of mod r |
| title_sub | faithful modules and generators of mod-R |
| topic | FPF rings Associative rings Modules (Algebra) Categories (Mathematics) Quasi-Frobenius-Ring (DE-588)4176637-4 gnd Ringtheorie (DE-588)4126571-3 gnd FPF-Ring (DE-588)4155116-3 gnd |
| topic_facet | FPF rings Associative rings Modules (Algebra) Categories (Mathematics) Quasi-Frobenius-Ring Ringtheorie FPF-Ring |
| url | https://doi.org/10.1017/CBO9780511721250 |
| work_keys_str_mv | AT faithcarl fpfringtheoryfaithfulmodulesandgeneratorsofmodr AT pagestanley fpfringtheoryfaithfulmodulesandgeneratorsofmodr |