A Course in Commutative Algebra
Springer 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.
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affine algebra affine domain affine variety algebraically closed field algebraically independent algorithm Artinian associated graded ring assume bijection chain of prime Chapter closure coefficients commutative algebra computing contained coordinate ring Corollary curve Dedekind domain defined definition degree dim(A dim(R dim(X divisor elements equation equidimensional example Exercise exists factorization field extension finitely follows formal power series fractional ideal gr(R Gröbner basis Hilbert function Hilbert series homogeneous homomorphism ht(P ht(Q hypothesis implies indeterminates induction integral domain intersection invertible irreducible subsets isomorphic Jacobian K-algebra K[x1 x n K|al Krull dimension LM(f LM(g maximal ideal minimal prime ideals module monomial ordering morphism Noether normalization Noetherian ring nonsingular nonzero normal form polynomial ring power series ring Proof Proposition prove Quot(R R-module radical ideal regular local ring Spec Spec(R subalgebra submodules surjective system of parameters Theorem 5.9 yields Zariski topology zero