Download One-Dimensional Cohen-Macaulay Rings by Eben Matlis PDF

By Eben Matlis

Show description

Read or Download One-Dimensional Cohen-Macaulay Rings PDF

Similar algebra books

Groebner bases algorithm: an introduction

Groebner Bases is a method that gives algorithmic suggestions to quite a few difficulties in Commutative Algebra and Algebraic Geometry. during this introductory educational the fundamental algorithms in addition to their generalization for computing Groebner foundation of a collection of multivariate polynomials are awarded.

The Racah-Wigner algebra in quantum theory

The improvement of the algebraic facets of angular momentum conception and the connection among angular momentum concept and particular subject matters in physics and arithmetic are lined during this quantity.

Wirtschaftsmathematik für Studium und Praxis 1: Lineare Algebra

Die "Wirtschaftsmathematik" ist eine Zusammenfassung der in den Wirtschaftswissenschaften gemeinhin benötigten mathematischen Kenntnisse. Lineare Algebra führt in die Vektor- und Matrizenrechnung ein, stellt Lineare Gleichungssysteme vor, berichtet über Determinanten und liefert Grundlagen der Eigenwerttheorie und Aussagen zur Definitheit von Matrizen.

Additional info for One-Dimensional Cohen-Macaulay Rings

Sample text

Y ( A such that xy = b is a r e g u l a r (3) A ®R Q is the full Proof. (1) = > is a r e g u l a r (1). If x is a r e g u l a r of A. element of A, then Ax ideal of R by y ~ A such that yx = b is a r e g u l a r of R. (1). of J. By Let J be a r e g u l a r (2) there J O R is a r e g u l a r (2) = > (3). of A, then X = z/x, (2) t h e r e ideal is an e l e m e n t H e n c e k = z y / x y = zy/b. t h e r e is an e l e m e n t 1/x = y/b. 2. ring of q u o t i e n t s element of A. b o t h b and y are r e g u l a r expression ring of q u o t i e n t s Let x be a r e g u l a r element y ¢ A and a r e g u l a r J A R is a r e g u l a r in the for k shows that of A.

17. Let A be a torsion d i v i s i b l e R-module. a sum of Artinian divisible Proof. Corollary R-modules. 3.

Be a chain of divisible c HomR(K,D2) c ... 7. by the proof of (3) ~ > H-module HomR(K,Dm) c of D. 6. Thus there is an index m 0 such that = HomR(K,Dmo ) for all m _> m O. 3, p r o v i n g Therefore D m = Dm0 for all that D has ACC on divisible submod- ules. (6) -~-> (I). 3 there is an R - h o m o m o r p h i s m Since K is Artinian submodule by (3) = > and hence f(K) c A. (7). This is a trivial (7) = > (5). It is a consequence R-modules. submodules, Suppose divisible We assert divisible submodule implication.

Download PDF sample

Rated 4.64 of 5 – based on 7 votes