A ring R (associative with identity) is abelian if each idempotent in R IS central; it is reduced
if it has no nonzero nilpotent elements; it is semicommutative if whenever elements a, b in R …

In this note we concern the structures of Armendariz rings and semicommutative rings which
are generalizations of reduced rings, the classical right quotient rings of Armendariz rings …

The term a ring means an associative ring with identity, and a general ring means an
associative ring with or without identity. But every definition for a ring can be applicable to a …

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 …

Throughout this paper, all rings are associative with identity. Given a wx ring R, the
polynomial ring over R is denoted by R x. This paper concerns the relationships between …

1. Introduction In [1 6], Rege and Chhawchharia introduced the notion of an Armendariz ring.
A ring R is called Armendariz if for any f (x)=∑ ni= 0 aixi, g (x)=∑ sj= 0 bjxj∈ R [x], f (x) g (x) …

We say a module MR a semicommutative module if for any m 2 M and any a 2 R, ma= 0
implies mRa= 0. This paper gives various properties of reduced, Armendariz, Baer, Quasi …

We introduce weak Armendariz rings which are a generalization of semicommutative rings
and Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is …

For a monoid M, we introduce nil-Armendariz rings relative to M, which are a generalization
of nil-Armendariz and M-Armendariz rings, and investigate their properties. First we show …

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 …