Search Results

You are looking at 1 - 3 of 3 items for :

  • Author or Editor: Ebrahim Hashemi x
  • Mathematics and Statistics x
  • All content x
Clear All Modify Search

A ring R is called right zip provided that if the right annihilator r R(X) of a subset X of R is zero, then there exists a finite subset Y of X, such that r R(Y) = 0. Faith [6] raised the following questions: When does R being a right zip ring imply R[x] being right zip?; When does R being a right zip imply R[G] being right zip when G is a finite group?; Characterize a ring R such that Mat n(R) is right zip. In this note we continue the study of the extensions of non-commutative zip rings based on Faith’s questions. It is shown that if R is a right McCoy ring, then R is right zip if and only if R[x] is a right zip ring. Also, if M is a strictly totally ordered monoid and R a right duo ring or a reversible ring, then R is right zip if and only if R[M] is right zip. As a consequence we obtain a generalization of [7].

Restricted access

A ring R is called right principally quasi-Baer (or simply right p.q.-Baer ) if the right annihilator of a principal right ideal of R is generated by an idempotent. Let R be a ring such that all left semicentral idempotents are central. Let α be an endomorphism of R which is not assumed to be surjective and R be α -compatible. It is shown that the skew power series ring R [[ x; α ]] is right p.q.-Baer if and only if the skew Laurent power series ring R [[ x, x −1 ; α ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any countable family of idempotents in R has a generalized join in I ( R ). An example showing that the α -compatible condition on R is not superfluous, is provided.

Restricted access

Abstract

The intersection of all maximal right ideals of a near-ring N is called the quasi-radical of N. In this paper, first we show that the quasi-radical of the zero-symmetric near-ring of polynomials R 0[x] equals to the set of all nilpotent elements of R 0[x], when R is a commutative ring with Nil (R)2 = 0. Then we show that the quasi-radical of R 0[x] is a subset of the intersection of all maximal left ideals of R 0[x]. Also, we give an example to show that for some commutative ring R the quasi-radical of R 0[x] coincides with the intersection of all maximal left ideals of R 0[x]. Moreover, we prove that the quasi-radical of R 0[x] is the greatest quasi-regular (right) ideal of it.

Restricted access