Some chain conditions on weak incidence algebras

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