Commutative Algebra with a View Toward Algebraic GeometryThis is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. |
Contents
Introduction | 1 |
Elementary Definitions | 11 |
The Dimension of Affine Rings | 13 |
Copyright | |
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Common terms and phrases
affine ring algebraic set algebraically closed field algorithm annihilator Artinian associated prime Chapter codim codimension coefficient field commutative algebra compute containing coordinate ring Corollary corresponding curve defined definition degree dimension domain elements equation exact sequence example Exercise factorization fiber filtration finite length finitely generated R-module flat follows free module geometric given graded ring Gröbner basis Hilbert function homogeneous ideal homomorphism idempotents in(g induction integral closure intersection invertible irreducible isomorphism kernel Krull linear M₁ matrix maximal ideal minimal primes monic monomial ideal monomial order monomorphism morphism multiplication Nakayama's lemma Noetherian ring nonzero nonzerodivisor normal Nullstellensatz polynomial ring primary decomposition prime ideal projective Proof Proposition prove quotient field R-algebra R-module R₁ regular local ring result Show statement submodule subring subset Suppose syzygies tensor theory topology unique variables variety vector space write Zariski