A module MR is called right principally quasi-Baer (or simply right p.q.-Baer) if the right annihilator of a principal submodule of R is generated by an idempotent. Let R be a ring. Let α be an endomorphism of R and MR be a α-compatible module and T = R[[x;α]]. It is shown that M [[x]]T is right p.q.-Baer if and only if MR is right p.q.-Baer and the right annihilator of any countably-generated ...

It is shown that in an infinite-dimensional dually separated second category topological vector space X there does not exist a probability measure μ for which the kernel coincides with X. Moreover, we show that in “good” cases the kernel has the full measure if and only if it is finitedimensional. Also, the problem posed by S. Chevet [5, p. 69] is solved by proving that the annihilator of the k...

we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...

Throughout the paper, all rings are associative rings with identity 1. The set of all idempotents of a ring R is denoted by E(R). Also, for a subset X ⊆ R, we denote the right [resp., left] annihilator of X by r(X) [resp., (X)]. We call a ring R a left p.p.-ring [3], in brevity, an l.p.p.-ring, if every principal left ideal of R, regarded as a left R-module, is projective. Dually, we may define...