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