International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 15, Pages 2389-2397
doi:10.1155/IJMMS.2005.2389
Some chain conditions on weak incidence algebras.
Surjeet Singh
and Fawzi Al-Thukair
Department of Mathematics, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Abstract
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)={x∈X:x≤z for some z∈Z}, 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.