Undergraduate commutative algebra:
Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic no...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1995
|
| Series: | London Mathematical Society student texts
29 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world |
| Physical Description: | 1 Online-Ressource (xiii, 153 Seiten) |
| ISBN: | 9781139172721 |
| DOI: | 10.1017/CBO9781139172721 |
Staff View
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
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| genre_facet | Einführung |
| id | DE-604.BV043940763 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9781139172721 |
| language | English |
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| publishDate | 1995 |
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| publisher | Cambridge University Press |
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| spelling | Reid, Miles 1948- Verfasser (DE-588)14377817X aut Undergraduate commutative algebra Miles Reid, University of Warwick Cambridge Cambridge University Press 1995 1 Online-Ressource (xiii, 153 Seiten) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society student texts 29 Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world Commutative algebra Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Kommutative Algebra (DE-588)4164821-3 s DE-604 Erscheint auch als Druck-Ausgabe, hardback 978-0-521-45255-7 Erscheint auch als Druck-Ausgabe, paperback 978-0-521-45889-4 https://doi.org/10.1017/CBO9781139172721 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Reid, Miles 1948- Undergraduate commutative algebra Commutative algebra Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4164821-3 (DE-588)4151278-9 |
| title | Undergraduate commutative algebra |
| title_auth | Undergraduate commutative algebra |
| title_exact_search | Undergraduate commutative algebra |
| title_full | Undergraduate commutative algebra Miles Reid, University of Warwick |
| title_fullStr | Undergraduate commutative algebra Miles Reid, University of Warwick |
| title_full_unstemmed | Undergraduate commutative algebra Miles Reid, University of Warwick |
| title_short | Undergraduate commutative algebra |
| title_sort | undergraduate commutative algebra |
| topic | Commutative algebra Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Commutative algebra Kommutative Algebra Einführung |
| url | https://doi.org/10.1017/CBO9781139172721 |
| work_keys_str_mv | AT reidmiles undergraduatecommutativealgebra |