Free ideal rings and localization in general rings:
Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2006
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| Schriftenreihe: | New mathematical monographs
3 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xxii, 572 pages) |
| ISBN: | 9780511542794 |
| DOI: | 10.1017/CBO9780511542794 |
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| 100 | 1 | |a Cohn, P. M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Free ideal rings and localization in general rings |c P.M. Cohn |
| 246 | 1 | 3 | |a Free Ideal Rings & Localization in General Rings |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2006 | |
| 300 | |a 1 online resource (xxii, 572 pages) | ||
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| 490 | 0 | |a New mathematical monographs |v 3 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | 0 | |t Generalities on rings and modules |g 1 |t Principal ideal domains |g 2 |t Firs, semifirs and the weak algorithm |g 3 |t Factorization in semifirs |g 4 |t Rings with a distributive factor lattice |g 5 |t Modules over firs and semifirs |g 6 |t Centralizers and subalgebras |g 7 |t Skew fields of fractions |
| 520 | |a Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note | ||
| 650 | 4 | |a Rings (Algebra) | |
| 650 | 4 | |a Ideals (Algebra) | |
| 650 | 4 | |a Associative algebras | |
| 650 | 0 | 7 | |a Maßtheorie |0 (DE-588)4074626-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804176883599802368 |
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| any_adam_object | |
| author | Cohn, P. M. |
| author_facet | Cohn, P. M. |
| author_role | aut |
| author_sort | Cohn, P. M. |
| author_variant | p m c pm pmc |
| building | Verbundindex |
| bvnumber | BV043941610 |
| classification_rvk | SK 430 |
| collection | ZDB-20-CBO |
| contents | Generalities on rings and modules Principal ideal domains Firs, semifirs and the weak algorithm Factorization in semifirs Rings with a distributive factor lattice Modules over firs and semifirs Centralizers and subalgebras Skew fields of fractions |
| ctrlnum | (ZDB-20-CBO)CR9780511542794 (OCoLC)850057569 (DE-599)BVBBV043941610 |
| 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 | 3512.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511542794 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511542794 |
| language | English |
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| spelling | Cohn, P. M. Verfasser aut Free ideal rings and localization in general rings P.M. Cohn Free Ideal Rings & Localization in General Rings Cambridge Cambridge University Press 2006 1 online resource (xxii, 572 pages) txt rdacontent c rdamedia cr rdacarrier New mathematical monographs 3 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Generalities on rings and modules 1 Principal ideal domains 2 Firs, semifirs and the weak algorithm 3 Factorization in semifirs 4 Rings with a distributive factor lattice 5 Modules over firs and semifirs 6 Centralizers and subalgebras 7 Skew fields of fractions Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note Rings (Algebra) Ideals (Algebra) Associative algebras Maßtheorie (DE-588)4074626-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-85337-8 https://doi.org/10.1017/CBO9780511542794 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cohn, P. M. Free ideal rings and localization in general rings Generalities on rings and modules Principal ideal domains Firs, semifirs and the weak algorithm Factorization in semifirs Rings with a distributive factor lattice Modules over firs and semifirs Centralizers and subalgebras Skew fields of fractions Rings (Algebra) Ideals (Algebra) Associative algebras Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4074626-4 |
| title | Free ideal rings and localization in general rings |
| title_alt | Free Ideal Rings & Localization in General Rings Generalities on rings and modules Principal ideal domains Firs, semifirs and the weak algorithm Factorization in semifirs Rings with a distributive factor lattice Modules over firs and semifirs Centralizers and subalgebras Skew fields of fractions |
| title_auth | Free ideal rings and localization in general rings |
| title_exact_search | Free ideal rings and localization in general rings |
| title_full | Free ideal rings and localization in general rings P.M. Cohn |
| title_fullStr | Free ideal rings and localization in general rings P.M. Cohn |
| title_full_unstemmed | Free ideal rings and localization in general rings P.M. Cohn |
| title_short | Free ideal rings and localization in general rings |
| title_sort | free ideal rings and localization in general rings |
| topic | Rings (Algebra) Ideals (Algebra) Associative algebras Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Rings (Algebra) Ideals (Algebra) Associative algebras Maßtheorie |
| url | https://doi.org/10.1017/CBO9780511542794 |
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