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International Conference on Algebra and its Applications
March 25-28, 1999
Ohio University
Athens, OH, USA

Organizers
Dinh Van Huynh, S.K. Jain, Sergio Lopez-Permouth

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On rings with chain conditions
by
S. Tariq Rizvi
The Ohio State University-Lima
Coauthors: D. V. Huynh

We investigate rings with special module decompositions M = P \oplusQ where P is projective and Q has some special properties .

We obtain a new characterization of noetherian rings: A ring R is right noetherian if and only if every cyclic right R-module is a direct sum of a projective module P and a module Q where Q is either injective or noetherian.

Certain classes of right artinian rings with "nice" properties are obtained via similar special decompositions of modules.

Date received: March 4, 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 # cabw-87.