A guide to groups, rings, and fields /:
This Guide offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together. It will be useful to both students and professionals. In addition t...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Washington, DC :
Mathematical Association of America,
2012.
|
| Schriftenreihe: | Dolciani mathematical expositions ;
no. 48. MAA guides ; no. 8. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This Guide offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together. It will be useful to both students and professionals. In addition to the standard material on groups, rings, modules, fields, and Galois theory, the book includes discussions of other important topics that are often omitted in the standard graduate course, including linear groups, group representations, the structure of Artinian rings, projective, injective and flat modules, Dedekind domains, and central simple algebras. All of the important theorems are discussed, without proofs but often with a discussion of the intuitive ideas behind those proofs. Those looking for a way to review and refresh their basic algebra will benefit from reading this Guide, and it will also serve as a ready reference for mathematicians who make use of algebra in their work. |
| Beschreibung: | 1 online resource (xvii, 309 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781614442110 1614442118 |
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| 505 | 0 | |a Algebra : classical, modern, and ultramodern ; Categories ; Algebraic structures ; Groups and their representations ; Rings and modules ; Fields and skew fields. | |
| 588 | 0 | |a Print version record. | |
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| author | Gouvêa, Fernando Q. (Fernando Quadros) |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:08Z |
| institution | BVB |
| isbn | 9781614442110 1614442118 |
| language | English |
| oclc_num | 823766426 |
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| series | Dolciani mathematical expositions ; MAA guides ; |
| series2 | Dolciani mathematical expositions ; MAA guides ; |
| spelling | Gouvêa, Fernando Q. (Fernando Quadros), author. https://id.oclc.org/worldcat/entity/E39PBJdGRqhFFCqbVB4rv7FFrq http://id.loc.gov/authorities/names/nr89016505 A guide to groups, rings, and fields / Fernando Q. Gouvêa. Washington, DC : Mathematical Association of America, 2012. 1 online resource (xvii, 309 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Dolciani mathematical expositions ; #48 MAA guides ; #8 Includes bibliographical references and index. Algebra : classical, modern, and ultramodern ; Categories ; Algebraic structures ; Groups and their representations ; Rings and modules ; Fields and skew fields. Print version record. This Guide offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together. It will be useful to both students and professionals. In addition to the standard material on groups, rings, modules, fields, and Galois theory, the book includes discussions of other important topics that are often omitted in the standard graduate course, including linear groups, group representations, the structure of Artinian rings, projective, injective and flat modules, Dedekind domains, and central simple algebras. All of the important theorems are discussed, without proofs but often with a discussion of the intuitive ideas behind those proofs. Those looking for a way to review and refresh their basic algebra will benefit from reading this Guide, and it will also serve as a ready reference for mathematicians who make use of algebra in their work. Algebra. http://id.loc.gov/authorities/subjects/sh85003425 Rings (Algebra) http://id.loc.gov/authorities/subjects/sh85114140 Algebraic fields. http://id.loc.gov/authorities/subjects/sh85048127 Algèbre. Anneaux (Algèbre) Corps algébriques. algebra. aat MATHEMATICS Algebra Intermediate. bisacsh Algebra fast Algebraic fields fast Rings (Algebra) fast Algebraische Gruppe gnd http://d-nb.info/gnd/4001164-1 Ring Mathematik gnd http://d-nb.info/gnd/4128084-2 Feld Mathematik gnd http://d-nb.info/gnd/4280861-3 Print version: Gouvea, Fernando Q. Guide to groups, rings, and fields. Washington : Mathematical Assn America, 2012 0883853558 (OCoLC)823041999 Dolciani mathematical expositions ; no. 48. http://id.loc.gov/authorities/names/n42009859 MAA guides ; no. 8. http://id.loc.gov/authorities/names/no2008118779 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=502758 Volltext |
| spellingShingle | Gouvêa, Fernando Q. (Fernando Quadros) A guide to groups, rings, and fields / Dolciani mathematical expositions ; MAA guides ; Algebra : classical, modern, and ultramodern ; Categories ; Algebraic structures ; Groups and their representations ; Rings and modules ; Fields and skew fields. Algebra. http://id.loc.gov/authorities/subjects/sh85003425 Rings (Algebra) http://id.loc.gov/authorities/subjects/sh85114140 Algebraic fields. http://id.loc.gov/authorities/subjects/sh85048127 Algèbre. Anneaux (Algèbre) Corps algébriques. algebra. aat MATHEMATICS Algebra Intermediate. bisacsh Algebra fast Algebraic fields fast Rings (Algebra) fast Algebraische Gruppe gnd http://d-nb.info/gnd/4001164-1 Ring Mathematik gnd http://d-nb.info/gnd/4128084-2 Feld Mathematik gnd http://d-nb.info/gnd/4280861-3 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85003425 http://id.loc.gov/authorities/subjects/sh85114140 http://id.loc.gov/authorities/subjects/sh85048127 http://d-nb.info/gnd/4001164-1 http://d-nb.info/gnd/4128084-2 http://d-nb.info/gnd/4280861-3 |
| title | A guide to groups, rings, and fields / |
| title_auth | A guide to groups, rings, and fields / |
| title_exact_search | A guide to groups, rings, and fields / |
| title_full | A guide to groups, rings, and fields / Fernando Q. Gouvêa. |
| title_fullStr | A guide to groups, rings, and fields / Fernando Q. Gouvêa. |
| title_full_unstemmed | A guide to groups, rings, and fields / Fernando Q. Gouvêa. |
| title_short | A guide to groups, rings, and fields / |
| title_sort | guide to groups rings and fields |
| topic | Algebra. http://id.loc.gov/authorities/subjects/sh85003425 Rings (Algebra) http://id.loc.gov/authorities/subjects/sh85114140 Algebraic fields. http://id.loc.gov/authorities/subjects/sh85048127 Algèbre. Anneaux (Algèbre) Corps algébriques. algebra. aat MATHEMATICS Algebra Intermediate. bisacsh Algebra fast Algebraic fields fast Rings (Algebra) fast Algebraische Gruppe gnd http://d-nb.info/gnd/4001164-1 Ring Mathematik gnd http://d-nb.info/gnd/4128084-2 Feld Mathematik gnd http://d-nb.info/gnd/4280861-3 |
| topic_facet | Algebra. Rings (Algebra) Algebraic fields. Algèbre. Anneaux (Algèbre) Corps algébriques. algebra. MATHEMATICS Algebra Intermediate. Algebra Algebraic fields Algebraische Gruppe Ring Mathematik Feld Mathematik |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=502758 |
| work_keys_str_mv | AT gouveafernandoq aguidetogroupsringsandfields AT gouveafernandoq guidetogroupsringsandfields |