We study the structure of rings which satisfy the von Neumann regularity of commutators,
and call a ring R C-regular if ab− ba∈(ab− ba) R (ab− ba) for all a, b in R. For a C-regular …

We study the structure of right regular commutators, and call a ring $ R ${\it strongly $ C $-
regular} if $ ab-ba\in (ab-ba)^ 2R $ for any $ a, b\in R $. We first prove that a …

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 …

The purpose of this note is to consider certain connections between injectivity, p-injectivity
and a generalisation of quasi-injectivity noted GQ-injectivity (cf. definition below). It is proved …

Let R be a commutative ring with 1 0. Then Z (R) denotes the set of all zerodivisors of R, Id
(R) denotes the set of all idempotent elements of R, U (R) denotes the set of all units of R …

The purpose of this thesis is to develop a general theory of regularities for rings. In ring
theory many so-called regularities appear. The oldest one seems to be the von Neumann …

We study the one-sided regularity of matrices in upper triangular matrix rings in relation with
the structure of diagonal entries. We next consider a ring theoretic condition that ab being …

1* Introduction* An important theorem in commutative ring theory is that if/is an ideal in a
Noetherian ring and if/consists entirely of zero divisors, then the annihilator of I is nonzero …

Introduction. Let K be a ring with 1 and acK. If for every bcK there exist r, hcK such that ab=
ra and ba= ah, then a is called semicommutative. If every element of K is semicommutative …

A commutative ring R has Property (A) if every finitely generated ideal of R consisting
entirely of zero-divisors has a nonzero annihilator. We continue in this paper the study of …