An introduction to abstract algebra: sets, groups, rings, and fields
"This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level. It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Ded...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2022]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level. It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers. In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory. As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular. Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further"-- |
| Beschreibung: | xvii, 419 Seiten Illustrationen |
| ISBN: | 9789811246661 9789811247552 |
Internformat
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| 100 | 1 | |a Weintraub, Steven H. |d 1951- |e Verfasser |0 (DE-588)113001770 |4 aut | |
| 245 | 1 | 0 | |a An introduction to abstract algebra |b sets, groups, rings, and fields |c Steven H Weintraub (Lehigh University, USA) |
| 246 | 1 | 3 | |a Abstract algebra |
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo |b World Scientific |c [2022] | |
| 300 | |a xvii, 419 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 520 | 3 | |a "This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level. It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers. In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory. As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular. Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further"-- | |
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Datensatz im Suchindex
| _version_ | 1804185015559389184 |
|---|---|
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| author | Weintraub, Steven H. 1951- |
| author_GND | (DE-588)113001770 |
| author_facet | Weintraub, Steven H. 1951- |
| author_role | aut |
| author_sort | Weintraub, Steven H. 1951- |
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| building | Verbundindex |
| bvnumber | BV048875100 |
| classification_rvk | SK 200 |
| classification_tum | MAT 110 |
| ctrlnum | (OCoLC)1381309981 (DE-599)KXP1811738842 |
| dewey-full | 512/.02 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.02 |
| dewey-search | 512/.02 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV048875100 |
| illustrated | Illustrated |
| index_date | 2024-07-03T21:44:47Z |
| indexdate | 2024-07-10T09:48:31Z |
| institution | BVB |
| isbn | 9789811246661 9789811247552 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034139940 |
| oclc_num | 1381309981 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-91G DE-BY-TUM |
| physical | xvii, 419 Seiten Illustrationen |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Weintraub, Steven H. 1951- Verfasser (DE-588)113001770 aut An introduction to abstract algebra sets, groups, rings, and fields Steven H Weintraub (Lehigh University, USA) Abstract algebra New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2022] xvii, 419 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier "This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level. It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers. In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory. As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular. Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further"-- Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Dedekind-Ring (DE-588)4330659-7 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Ringtheorie (DE-588)4126571-3 gnd rswk-swf Körpertheorie (DE-588)4164455-4 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Ringtheorie (DE-588)4126571-3 s Galois-Theorie (DE-588)4155901-0 s Körpertheorie (DE-588)4164455-4 s Dedekind-Ring (DE-588)4330659-7 s DE-604 Erscheint auch als Online-Ausgabe 978-981-124-667-8 Erscheint auch als Online-Ausgabe 978-981-124-668-5 B:DE-89 V:DE-601 pdf/application https://www.gbv.de/dms/tib-ub-hannover/1811738842.pdf 2022-12-03 Inhaltsverzeichnis |
| spellingShingle | Weintraub, Steven H. 1951- An introduction to abstract algebra sets, groups, rings, and fields Gruppentheorie (DE-588)4072157-7 gnd Dedekind-Ring (DE-588)4330659-7 gnd Galois-Theorie (DE-588)4155901-0 gnd Ringtheorie (DE-588)4126571-3 gnd Körpertheorie (DE-588)4164455-4 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4330659-7 (DE-588)4155901-0 (DE-588)4126571-3 (DE-588)4164455-4 |
| title | An introduction to abstract algebra sets, groups, rings, and fields |
| title_alt | Abstract algebra |
| title_auth | An introduction to abstract algebra sets, groups, rings, and fields |
| title_exact_search | An introduction to abstract algebra sets, groups, rings, and fields |
| title_exact_search_txtP | An introduction to abstract algebra sets, groups, rings, and fields |
| title_full | An introduction to abstract algebra sets, groups, rings, and fields Steven H Weintraub (Lehigh University, USA) |
| title_fullStr | An introduction to abstract algebra sets, groups, rings, and fields Steven H Weintraub (Lehigh University, USA) |
| title_full_unstemmed | An introduction to abstract algebra sets, groups, rings, and fields Steven H Weintraub (Lehigh University, USA) |
| title_short | An introduction to abstract algebra |
| title_sort | an introduction to abstract algebra sets groups rings and fields |
| title_sub | sets, groups, rings, and fields |
| topic | Gruppentheorie (DE-588)4072157-7 gnd Dedekind-Ring (DE-588)4330659-7 gnd Galois-Theorie (DE-588)4155901-0 gnd Ringtheorie (DE-588)4126571-3 gnd Körpertheorie (DE-588)4164455-4 gnd |
| topic_facet | Gruppentheorie Dedekind-Ring Galois-Theorie Ringtheorie Körpertheorie |
| url | https://www.gbv.de/dms/tib-ub-hannover/1811738842.pdf |
| work_keys_str_mv | AT weintraubstevenh anintroductiontoabstractalgebrasetsgroupsringsandfields AT weintraubstevenh abstractalgebra |