Characterizations of strongly regular rings, II
Soukup Lajos, Ferenc Andor Szász · Proceedings of the Japan Academy Series A Mathematical Sciences · 1970
An associative ring A is called strongly regular if, for any element a of A, there exists an element x in A suoh that a-a2x.Characteri- zations of strongly regular rings were given by Andrunakievi6 [1], Lajos [5], Luh [8], and Schein[ 9], moreover by Lajos and SzAsz [7].This paper is connected with authors' earlier note [6].For the semi- group theoretical terminology we refer to Clifford and Preston [2].The purpose of this note is to give a further characterization of the class of strongly regular rings.For this aim we shall use four well known important propositions and in the proof of the theorem an equivalence relation discussed formerly by S. Lajos [3], which is a two-sided congruence relation on the multiplicative semigroup S of a strongly regular ring A.