Introduction To Commutative AlgebraCRC Press, 09.03.2018 - 140 Seiten First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization. |
Inhalt
Chapter 1 Rings and Ideals | 1 |
Chapter 2 Modules | 17 |
Chapter 3 Rings and Modules of Fraction | 36 |
Chapter 4 Primary Decomposition | 50 |
Chapter 5 Integral Dependence and Valuations | 59 |
Chapter 6 Chain Conditions | 74 |
Chapter 7 Noetherian Rings | 80 |
Chapter 8 Artin Rings | 89 |
Chapter 9 Discrete Valuation Rings and Dedekind Domains | 93 |
Chapter 10 Completions | 100 |
Chapter 11 Dimension Theory | 116 |
| 127 | |
Andere Ausgaben - Alle anzeigen
Introduction To Commutative Algebra, Student Economy Edition Michael Atiyah Eingeschränkte Leseprobe - 2018 |
Häufige Begriffe und Wortgruppen
A-algebra A-module algebraic apply Artin assume belonging called Chapter coefficients commutative completion composition condition Consider construction contains Conversely Corollary correspondence Dedekind domain Deduce defined denote dimension direct element equation exact sequence example Exercise exists extension field field of fractions finitely finitely-generated flat following are equivalent function geometry given gives graded hence identity induces injective integral domain integrally closed intersection inverse irreducible isomorphism Jacobson lemma length mapping maximal ideal module multiplicatively closed subset nilpotent Noetherian ring non-zero particular polynomial primary decomposition primary ideals prime ideal Proof Proposition Prove quotient radical Remark respect result ring homomorphism satisfies Show space Spec submodule subring Suppose surjective Take Theorem topology true unique unit valuation ring zero zero-divisor