Introduction. A von Neumann regular ring A may be characterised by any one of the
following conditions:(a) every right (left) A-module is flat;(b) every right (left) A-module is p …

In [1], S. Endo proved that if Л is a normal left pp ring, then for any ae A, there exist a central
indempotent e and a left. regular element d such that a= de. We prove that, in fact, normal pp …

A generalization of injectivity, caIled E-injectivity, is studied in connection with von Neumann
regular rings and continuous regular ring (in the sense of Y. Ulumi). Various pr. 야 rties of E …

Generalisations of von Neumann regular rings are considered through annihilators, purity
and certain special cyclic modules. Left self-injective regular, strongly regular and biregular …

Introduction and Notation. A ring R is called a (von Neumann) regular ring if for each a in R
there exists an x in R such that a= axa. The notion of regularity has been extended to …

Utumi has shown [3, Claim 5.1] that for a certain class of rings the associated maximal rings
of right quotients are isomorphic to the endomorphism rings of modules over division rings …

Throughout this paper R denotes associative with identity and all modules are unitary. J (R)
and Z,(R) denote the Jacobson radical and the singular right ideal of R, respectively. A right …

It is still unknown whether a SF-ring A (every simple left or right A-module is flat) is von
Neumann regular. The following non-trivial generalization of regular rings is considered …

Recently, in the Research Problems of Canadian Mathematical Bulletin, Vol. 14, No. 4,
1971, there appeared a problem which asks" Is a prime Von Neumann regular ring …

In analogy to the elementwise definition of von Neumann regular rings an $ R $-module $ M
$ is called regular if given any element $ m\in M $ there exists $ f\in {\operatorname {Hom} …