Krull-Schmidt theorems in dimension 1-Reference-Cited by-同舟云学术

Krull-Schmidt theorems in dimension 1

Published:1996 Issue:9 Volume:348 Page:3391-3455
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Levy Lawrence,Odenthal Charles

Abstract

Let Λ \Lambda be a semiprime, module-finite algebra over a commutative noetherian ring R R of Krull dimension 1. We find necessary and sufficient conditions for the Krull-Schmidt theorem to hold for all finitely generated Λ \Lambda -modules, and necessary and sufficient conditions for the Krull-Schmidt theorem to hold for all finitely generated torsionfree Λ \Lambda -modules (called “ Λ \Lambda -lattices” in integral representation theory, and “maximal Cohen-Macaulay modules” in the dimension-one situation in commutative algebra).

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1996-348-09/S0002-9947-96-01619-4/S0002-9947-96-01619-4.pdf

Reference25 articles.

1. Finitistic dimension and a homological generalization of semi-primary rings;Bass, Hyman;Trans. Amer. Math. Soc.,1960

2. Pure and Applied Mathematics;Curtis, Charles W.,1981

3. Krull-Schmidt and cancellation over local rings;Evans, E. Graham, Jr.;Pacific J. Math.,1973

4. Integral representations and diagrams;Green, E. L.;Michigan Math. J.,1978

Cited by 19 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Generalized lattices over one-dimensional noetherian domains;Journal of Commutative Algebra;2022-11-01

2. Cancellation of finite-dimensional Noetherian modules;Journal of Algebra;2022-09

3. Lattices over Bass Rings and Graph Agglomerations;Algebras and Representation Theory;2021-03-15

4. Unique decomposition into ideals for commutative Noetherian rings;Journal of Pure and Applied Algebra;2020-09

5. Serial Nonsingular Rings. Jacobsons’s Conjecture;Algebras, Rings and Modules;2016-04-05