Undergraduate commutative algebra /
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| Author / Creator: | Reid, Miles (Miles A.) |
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| Imprint: | Cambridge ; New York : Cambridge University Press, 1995. |
| Description: | 1 online resource (xiii, 153 pages) : illustrations |
| Language: | English |
| Series: | London Mathematical Society student texts ; 29 London Mathematical Society student texts ; 29. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/12355879 |
| 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. |
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| Physical Description: | 1 online resource (xiii, 153 pages) : illustrations |
| Bibliography: | Includes bibliographical references (page 149) and index. |
| ISBN: | 9781139172721 1139172727 0521452554 9780521452557 0521458897 9780521458894 |
