The semicommutative property of rings was introduced ini-tially by Bell, and has done
important roles in noncommutative ring the-ory. This concept was generalized to one of nil …

In this paper, we study the properties of Ore extensions of nil-semicommutative rings. Let α
be an endomorphism and δ an α-derivation of a ring R. By using the itemized analysis …

In this paper, we study the properties of Ore extensions of nil-semicommutative rings. Let α
be an endomorphism and δ an α-derivation of a ring R. By using the itemized analysis …

Semicommutative and Armendariz rings are a generalization of reduced rings, and
therefore, nilpotent elements play an important role in this class of rings. There are many …

This note is concerned with generalizations of commutativity. We introduce identity-
symmetric and right near-commutative, and study basic structures of rings with such ring …

In this note a ring R is defined to be nil-semicommutative in case for any a, b∈ R, ab is
nilpotent implies that arb is nilpotent whenever r∈ R. Examples of such rings include …

We study the structure of the set of nilpotent elements in extended semicommutative rings
and introduce nil α-semicommutative rings as a generalization. We resolve the structure of …

A ring R is said to be weakly semicommutative if for any a, b∈ R, ab= 0 implies aRb⊆ Nil
(R), where Nil (R) is the set of all nilpotent elements in R. In this note, we clarify the …

The reflexive property for ideals was introduced by Mason and has important roles in
noncommutative ring theory. In this note we study the structure of idempotents satisfying the …

A ring R is defined to be nil-semicommutative if ab\in N (R) implies arb\in N (R) for a, b, r\in
R, where N (R) stands for the set of nilpotents of R. Nil-semicommutative rings are …