On the regularity-preserving elements in regular LA** -semigroups

Abstract

In this paper, the notions of regularity-preserving elements in left almost semigroups are investigated. Moreover, we prove that the following conditions are equivalent.

1. a is a regularity-preserving element in a regular LA**-semigroup.
2. $(b*a)* S= S*b$ for any element  b of S.
3. $a\in R(S)$.

Finally, we characterize the regularity-preserving elements of regular LA**-semigroups.