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Ring Theory Session of the fourth joint meeting of the American Mathematical Society and the Sociedad Matematica Mexicana
May 19-22, 1999
University of North Texas
Denton, TX, USA

Organizers
Ricardo Alfaro, Carlos Signoret, Sergio R. Lopez-Permouth

View Abstracts

Chain Conditions on Quotient Finite (Uniform) Dimensional Modules
by
Toma Albu
The Ohio State University
Coauthors: S. Tariq Rizvi

This paper is motivated by the recent work of C. Faith, Quotient finite dimensional modules with ACC on subdirectly irreducible submodules are Noetherian (to appear in Comm. Algebra, 1999), who has proved that a quotient finite dimensional module which satisfies the ascending chain condition on subdirectly irreducible submodules is Noetherian. A natural question to ask is whether its dual holds true. We answer this in the affirmative, and provide a characterization of Artinian modules dual to Faith's Theorem. We also extend these results to the more general settings involving dual Krull dimension and Krull dimension respectively.

Date received: March 24, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabz-15.