Introduction To Commutative Algebra, Student Economy EditionCRC Press, 27.04.2018 - 140 Seiten This book is designed to be read by students who have had a first elementary course in general algebra. It provides a common generalization of the primes of arithmetic and the points of geometry. The book explains the various elementary operations which can be performed on ideals. |
Inhalt
Introduction | |
Modules | |
Rings and Modales of Fractions | |
Primary Decomposition | |
Integral Dependence and Valuations | |
Chain Conditions | |
Noetherian Rings | |
Artin Rings | |
Completions | |
Dimension Theory | |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
A-algebra a-filtration A-module homomorphism abelian group Artin ring Artinian chain of prime Chapter closure coefficients commutative algebra composition series coprime Corollary Dedekind domain Deduce defined denote dimension direct limit discrete valuation ring equation exact sequence example exists field of fractions finitely generated A-module finitely-generated A-module following are equivalent fractional ideal graded ring Hausdorff hence induction injective integral domain integrally closed intersection inverse irreducible isomorphism Jacobson radical kernel lemma Let f mapping maximal element maximal ideal minimal primary decomposition minimal prime ideal module multiplicatively closed subset nilpotent nilradical Noetherian local ring Noetherian ring p-primary polynomial ring primary decomposition primary ideals prime ideals belonging principal ideal Proof Proposition Prove quotient residue field resp ring and let ring homomorphism satisfies Show Spec subgroup submodule subring subspace Suppose surjective tensor product Theorem topology vector space zero ideal zero-divisor