A Course in Commutative AlgebraSpringer Science & Business Media, 02.12.2010 - 248 Seiten This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text. |
Inhalt
| 2 | |
| 6 | |
Part II Dimension | 49 |
Part III Computational Methods | 115 |
Part IV Local Rings | 165 |
Solutions of Some Exercises | 217 |
| 235 | |
| 239 | |
| 241 | |
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Häufige Begriffe und Wortgruppen
affine algebra affine variety algorithm Applying Artinian assume called Chapter complete computing conclude condition consider constructible contained converse coordinate ring Corollary correspondence curve Dedekind domain defined definition dim(R dimension elements equality equation equivalent example Exercise exists extension fact factorization fiber field finitely follows fractional function given gives going gr(R graded Gröbner basis height holds homomorphism hypothesis implies indeterminates induction integral integral domain intersection invertible irreducible isomorphic K-algebra K[x1 x n K|al leading Lemma length lies localization maximal ideal means minimal module monomial ordering morphism multiplicative Noether Noetherian Noetherian ring nonzero normal obtain particular polynomial ring prime ideals principal ideal Proof Proposition prove R-module regular Remark respect result satisfies says separable Show space Spec(R statements submodules subset Theorem theory topology unique write yields zero