Artinian subrings of a commutative ring-Reference-Cited by-同舟云学术

Artinian subrings of a commutative ring

Published:1993 Issue:1 Volume:336 Page:295-310
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Gilmer Robert,Heinzer William

Abstract

Given a commutative ring R R , we investigate the structure of the set of Artinian subrings of R R . We also consider the family of zero-dimensional subrings of R R . Necessary and sufficient conditions are given in order that every zero-dimensional subring of a ring be Artinian. We also consider closure properties of the set of Artinian subrings of a ring with respect to intersection or finite intersection, and the condition that the set of Artinian subrings of a ring forms a directed family.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1993-336-01/S0002-9947-1993-1102887-7/S0002-9947-1993-1102887-7.pdf

Reference18 articles.

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3. The converse to a well known theorem on Noetherian rings;Eakin, Paul M., Jr.;Math. Ann.,1968

4. Integral domains with Noetherian subrings;Gilmer, Robert;Comment. Math. Helv.,1970

5. Domains with integrally closed subrings;Gilmer, Robert;Math. Japon.,1971

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