In this paper, the notions of regularity-preserving elements in left almost semigroups are investigated. Moreover, we prove that the following conditions are equivalent.
a is a regularity-preserving element in a regular LA**-semigroup.
$(b*a)* S= S*b$ for any element b of S.
$a\in R(S)$.
Finally, we characterize the regularity-preserving elements of regular LA**-semigroups.
Keywords
left almost semigroup, -semigroup, regularity-preserving element, left invertive, regular left almost semigroup