Rings and Categories of Modules:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1974
|
| Schriftenreihe: | Graduate Texts in Mathematics
13 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Art in Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semiperfect and perfect rings. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course, many important areas of ring and module theory that the text does not touch upon. For example, we have made no attempt to cover such subjects as homology, rings of quotients, or commutative ring theory |
| Beschreibung: | 1 Online-Ressource (IX, 339 p) |
| ISBN: | 9781468499131 9780387900704 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-9913-1 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042421238 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1974 |||| o||u| ||||||eng d | ||
| 020 | |a 9781468499131 |c Online |9 978-1-4684-9913-1 | ||
| 020 | |a 9780387900704 |c Print |9 978-0-387-90070-4 | ||
| 024 | 7 | |a 10.1007/978-1-4684-9913-1 |2 doi | |
| 035 | |a (OCoLC)864074922 | ||
| 035 | |a (DE-599)BVBBV042421238 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 510 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Anderson, Frank W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Rings and Categories of Modules |c by Frank W. Anderson, Kent R. Fuller |
| 264 | 1 | |a New York, NY |b Springer New York |c 1974 | |
| 300 | |a 1 Online-Ressource (IX, 339 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Graduate Texts in Mathematics |v 13 |x 0072-5285 | |
| 500 | |a This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Art in Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semiperfect and perfect rings. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course, many important areas of ring and module theory that the text does not touch upon. For example, we have made no attempt to cover such subjects as homology, rings of quotients, or commutative ring theory | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Physics | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Physics, general | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Kategorie |g Mathematik |0 (DE-588)4129930-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Modul |0 (DE-588)4129770-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ring |g Mathematik |0 (DE-588)4128084-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Ring |g Mathematik |0 (DE-588)4128084-2 |D s |
| 689 | 0 | 1 | |a Modul |0 (DE-588)4129770-2 |D s |
| 689 | 0 | 2 | |a Kategorie |g Mathematik |0 (DE-588)4129930-9 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Fuller, Kent R. |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4684-9913-1 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027856655 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153094064308224 |
|---|---|
| any_adam_object | |
| author | Anderson, Frank W. |
| author_facet | Anderson, Frank W. |
| author_role | aut |
| author_sort | Anderson, Frank W. |
| author_variant | f w a fw fwa |
| building | Verbundindex |
| bvnumber | BV042421238 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)864074922 (DE-599)BVBBV042421238 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-9913-1 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03194nmm a2200529zcb4500</leader><controlfield tag="001">BV042421238</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1974 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781468499131</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4684-9913-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387900704</subfield><subfield code="c">Print</subfield><subfield code="9">978-0-387-90070-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4684-9913-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)864074922</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042421238</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Anderson, Frank W.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Rings and Categories of Modules</subfield><subfield code="c">by Frank W. Anderson, Kent R. Fuller</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer New York</subfield><subfield code="c">1974</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (IX, 339 p)</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">Graduate Texts in Mathematics</subfield><subfield code="v">13</subfield><subfield code="x">0072-5285</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Art in Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semiperfect and perfect rings. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course, many important areas of ring and module theory that the text does not touch upon. For example, we have made no attempt to cover such subjects as homology, rings of quotients, or commutative ring theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Physics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kategorie</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4129930-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Modul</subfield><subfield code="0">(DE-588)4129770-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ring</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4128084-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Ring</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4128084-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Modul</subfield><subfield code="0">(DE-588)4129770-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Kategorie</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4129930-9</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="700" ind1="1" ind2=" "><subfield code="a">Fuller, Kent R.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4684-9913-1</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027856655</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></record></collection> |
| id | DE-604.BV042421238 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468499131 9780387900704 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856655 |
| oclc_num | 864074922 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (IX, 339 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Graduate Texts in Mathematics |
| spelling | Anderson, Frank W. Verfasser aut Rings and Categories of Modules by Frank W. Anderson, Kent R. Fuller New York, NY Springer New York 1974 1 Online-Ressource (IX, 339 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 13 0072-5285 This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Art in Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semiperfect and perfect rings. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course, many important areas of ring and module theory that the text does not touch upon. For example, we have made no attempt to cover such subjects as homology, rings of quotients, or commutative ring theory Mathematics Physics Mathematics, general Physics, general Mathematik Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Modul (DE-588)4129770-2 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 s Modul (DE-588)4129770-2 s Kategorie Mathematik (DE-588)4129930-9 s 1\p DE-604 Fuller, Kent R. Sonstige oth https://doi.org/10.1007/978-1-4684-9913-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Anderson, Frank W. Rings and Categories of Modules Mathematics Physics Mathematics, general Physics, general Mathematik Kategorie Mathematik (DE-588)4129930-9 gnd Modul (DE-588)4129770-2 gnd Ring Mathematik (DE-588)4128084-2 gnd |
| subject_GND | (DE-588)4129930-9 (DE-588)4129770-2 (DE-588)4128084-2 |
| title | Rings and Categories of Modules |
| title_auth | Rings and Categories of Modules |
| title_exact_search | Rings and Categories of Modules |
| title_full | Rings and Categories of Modules by Frank W. Anderson, Kent R. Fuller |
| title_fullStr | Rings and Categories of Modules by Frank W. Anderson, Kent R. Fuller |
| title_full_unstemmed | Rings and Categories of Modules by Frank W. Anderson, Kent R. Fuller |
| title_short | Rings and Categories of Modules |
| title_sort | rings and categories of modules |
| topic | Mathematics Physics Mathematics, general Physics, general Mathematik Kategorie Mathematik (DE-588)4129930-9 gnd Modul (DE-588)4129770-2 gnd Ring Mathematik (DE-588)4128084-2 gnd |
| topic_facet | Mathematics Physics Mathematics, general Physics, general Mathematik Kategorie Mathematik Modul Ring Mathematik |
| url | https://doi.org/10.1007/978-1-4684-9913-1 |
| work_keys_str_mv | AT andersonfrankw ringsandcategoriesofmodules AT fullerkentr ringsandcategoriesofmodules |