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 …

We investigate von Neumann regularity of rings whose simple singular right R-modules are
GP-injective. It is proved that a ring; R is strongly regular iff R is a weakly right duo ring …

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 …

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 …

A ring R is called right weakly regular if for every elemwt x ER, x E xRxR. R is called weakly
regular if it is both right and left weakly regular. This concept was introduced by VS …

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 …

A well-known theorem of Kaplansky states that a commutative ring R is von Neumann
regular iff every simple R-module is injective. Rings whose simple singular modules are …

A CRITERION FOR UNIT-REGULARITY Page 1 Acta Math. Hungar., 111 (4) (2006), 311–312.
DOI: 10.1556/AMath.111.2006.4.3 A CRITERION FOR UNIT-REGULARITY G. MARKS …

(5)(1). In any rate, R is a reduced ring. If a2= aa'a= a'a2 then (a-aa') 2= 0, and hence a= aa'=
aba with some b. Similarly,(6)(1) and (7)(1).(b) It suffices to prove that (2) implies (1). In fact …

A note on regular modules Page 1 BULL. AUSTRAL. MATH. SOC. I6A30 VOL. II ( 1 9 7 4 ) , 3 5
9 - 3 6 4 . ( I 6 A 5 O ) A note on regular modules VS Ramamurthi Kaplansky's observation …