Since the discovery of the existence of the injective hull of an arbitrary module
independently in 1952 by Shoda and in 1953 by Eckmann and Schopf, there have been …

Ever since their introduction, skew PBW ($ Poincar {\acute {e}} $-Birkhoff-Witt) extensions of
rings have kept growing in importance, as researchers characterized their properties (such …

We say a ring R is π-Baer if the right annihilator of every projection invariant left ideal of R is
generated by an idempotent element of R. In this paper, we study connections between the …

Let R be a ring with a monomorphism α and an α-derivation δ. We introduce (α, δ)-weakly
rigid rings which are a generalisation of α-rigid rings and investigate their properties. Every …

We say that a*-ring R is a generalized quasi-Baer*-ring if for any ideal I of R, the right
annihilator of I n is generated, as a right ideal, by a projection, for some positive integer n …

A ring R is a left AIP-ring if the left annihilator of any ideal of R is pure as a left ideal.
Equivalently, R is a left AIP-ring if R modulo the left annihilator of any ideal is flat. This class …

A ring $ R $ with an automorphism $\sigma $ and a $\sigma $-derivation $\delta $ is called
$\delta $-quasi-Baer (resp., $\sigma $-invariant quasi-Baer) if the right annihilator of every …

Let α be an endomorphism of R which is not assumed to be surjective and R be α-
compatible. It is shown that the skew power series ring R [[x; α]] is right pq-Baer if and only if …

A ring R is called right\(\mathfrak {cP}\)-Baer if the right annihilator of a cyclic projective right
R-module in R is generated by an idempotent. These rings are a generalization of the right …

Let $ alpha $ be an endomorphism and $ delta $ an $ alpha $-derivationof a ring $ R $. In
this paper we study the relationship between an $ R $-module $ M_R $ and the general …