A ring R is called left P-injective if for every a∈ R, aR= r (l (a)) where l (⋅) and r (⋅) denote
left and right annihilators respectively. The ring R is called left GP-injective if for any 0≠ a∈ …

Let R be a ring with second singular right ideal and second singular left ideal. Motivated by a
result in Zhou (Zhou, Y.(2002). Rings in which certain right ideals are direct summands of …

Let $ R $ be a ring with identity. An ideal $ N $ of $ R $ is called $ ideal $-$ symmetric
$(resp., $ ideal $-$ reversible $) if $ ABC\subseteq N $ implies $ ACB\subseteq N $(resp …

A ring R with unity is called a (quasi-) Baer ring if the left annihilator of every (left ideal)
nonempty subset of R is generated (as a left ideal) by an idempotent. Armendariz has shown …

Let R be a ring. A left R-module M (resp. right R-module N) is called singly injective (resp.
singly flat) if Ext1 (F/C, M)= 0 (resp. Tor1 (N, F/C)= 0) for any cyclic submodule C of any …

An extension ring S of a ring T is called a left quotient ring of T if for any two elements ΛH= 0
and y of S there exists an element a of T such that ax^ rO and ay belongs to T. Let R be a …

In this paper, we introduce a new generalization of coherent rings. Let m be a positive
integer and da positive integer or d=∞. A ring R is called a left (m, d)-coherent ring in case …

Note that, if X is a subset of a ring R, l (X)(resp. r (X)) is just the left (resp. right) annihilator of
X in R since(RR)*= RR. We call a ring R right PF if every faithful right R-module is a …

Let R be an arbitrary ring and let M be a finitely generated right jR-module. Then the dual
module M*= HomR (M, R) of M is a left Λ-module. If R is a left noetherian ring or finite …

In this paper, we introduce a class of rings which is a generalization of symmetric rings.
Let\(R\) be a ring with identity. A ring\(R\) is called central symmetric if for any\(a\),\(b, c\in …