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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 15, Pages 2389-2397

Some chain conditions on weak incidence algebras

Department of Mathematics, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 19 March 2005; Revised 12 July 2005

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let X be any partially ordered set, R any commutative ring, and T=I(X,R) the weak incidence algebra of X over R. Let Z be a finite nonempty subset of X, L(Z)={xX:xz   for some   zZ}, and M=Tez. Various chain conditions on M are investigated. The results so proved are used to construct some classes of right perfect rings that are not left perfect.