The study of rings with right Property (A), has done an important role in noncommutative ring
theory. Following literature, a ring R has right Property (A) if every finitely generated two …

In this paper, we introduce a new kind of rings that behave like semicommutative rings, but
satisfy yet more known results. This kind of rings is called P-semicommutative. We prove that …

We study the structure of central elements in relation with polynomial rings and introduce
quasi-commutative as a generalization of commutative rings. The Jacobson radical of the …

An endomorphism α of a ring R is called semicommutative if ab= 0 implies aR α (b)= 0 for a,
b∈ R, and R is called an α-semicommutative ring if there exists a semicommutative …

In this paper, we focus on the semicommutative property of rings via idempotent elements. In
this direction, we introduce a class of rings, so-called right e-semicommutative rings. The …

The concept of nil‐symmetric rings has been introduced as a generalization of symmetric
rings and a particular case of nil‐semicommutative rings. A ring R is called right (left) nil …

The reversible property is an important role in noncommutative ring theory. Recently, the
study of the reversible ring property on nilpotent elements is established by Abdul-Jabbar et …

Let R be a ring with identity and an ideal I. In this paper, we introduce a class of rings
generalizing semicommutative rings which is called I-semicommutative. The ring R is called …

In this paper, we introduce a new concept in Nil-semicommutative modules and present it as
an extension of Nil-semicommutative rings to modules. We prove that the class of Nil …

A ring R is called weakly semicommutative ring if for any a, $ b {\in} R^* $= R\{0} with ab= 0,
there exists $ n {\geq} 1$ such that either an $ a^ n {\neq} 0$ and $ a^ nRb= 0$ or $ b^ n …