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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

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On the nilpotence of the \tau-closed prime radical in rings with \tau-Krull dimension
by
Günter R. Krause
Dept. of Mathematics, University of Manitoba
Coauthors: Toma Albu, Mark L. Teply

Necessary and sufficient conditions are provided for the nilpotence of the intersection of all \tau-closed prime ideals of a \tau-tosionfree ring R with \tau-Krull dimension, where \tau denotes a hereditary torsion theory on the category Mod-R of right R-modules. It is shown that these conditions hold, in particular, when \tau is ideal invariant. Furthermore, conditions are provided for Ass(M) to be non-empty for every nonzero \tau-torsionfree right R-module M.

Date received: March 21, 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-06.