A ring $R$ is called a left Ikeda-Nakayama (left IN-ring) if the right annihilator of intersection any two ideals sum annihilators. As generalization IN-rings, SA-ring annihilators an ideal $R$. It natural to ask IN and SA property can be extended from $R[x; \alpha, \delta]$. In this note, results concerning conditions will allow these properties transfer skew polynomials $R[x;\alpha,\delta]$ a...

Yoshizawa investigated when local cohomology modules have an annihilator that does not depend on the choice of defining ideal. In this paper we refine his results and investigate relationship between annihilators restricted flat dimensions.

Let R be a local Noetherian commutative ring. We prove that is an Artinian Gorenstein ring if and only every ideal in trace ideal. discuss when the of module coincides with its double annihilator.

A commutative ring R is said to satisfy property (P) if every finitely generated proper ideal of R admits a non-zero annihilator. In this paper we give some necessary and sufficient conditions that a ring satisfies property (P). In particular, we characterize coherent rings, noetherian rings and P-coherent rings with property (P).

The notion of the weighted (b,c)-inverse an element in rings were introduced very recently. In this paper, we further elaborate on theory by establishing a few characterizations inverse and their relationships with other (v,w)-weighted (b,c)-inverses. We discuss necessary sufficient conditions for existence hybrid annihilator (b, c)-inverse ring. addition, explore reverse-order law