Preface All rings are assumed to be associative and (except for nilrings and some stipulated
cases) to have nonzero identity elements. A ring A is said to be regular if for every element a …

This paper attempts to generalize a property of regular rings, namely, I2= I for every right
(left) ideal. Rings with this property are called right (left) weakly regular. A ring which is both …

1. Introduction. An element a of a ring 9Î is said to be regular if there exists an element x of dt
such that axa= a. A ring 9î with unit element, every element of which is regular, is a regular …

In [2] Henriksen proves that if R is a unit regular ring, then every matrix over R admits
diagonal reduction. On the other hand it is well known, cf.[l, 4.12; 4.13; 4.151, that a regular …

ON REGULARITY OF RINGS 1 Page 1 ON REGULARITY OF RINGS 1 Jianlong Chen Department
of Mathematics, Harbin Institute of Technology Harbin 150001, PR China and Department of …

A strongly regular ring R is one in which for all x∈ R, there is an a∈ R with x= x2a.
Equivalently, for all x there is an a with x= ax2. Such a ring is regular, duo, biregular, and a …

Recall that a ring R is said to be regular in the sense of yon Neumann if for every a ε R, there
is an x ε R such that axa= a. If, in addition, R has an identity element 1, and there is such an …

In this chapter we shall make a study of rings satisfying certain ascending chain conditions.
In the non-commutative case-and this is really the only case with which we shall be …

We shall consider certain (associative) rings R which are generalizations of regular rings (in
the sense of von Neumann): the m-regular,~-regular 1 etc. rings. In the present paper we …

A ring R is unit regular if for every $ a\in R $, there is a unit $ x\in R $ such that $ axa= a $,
and one-sided unit regular if for every $ a\in R $, there is a right or left invertible element …