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

  • Pairote Yiarayong Pibulsongkram Rajabhat University
  • Chadarat Tapan
Keywords: left almost semigroup, -semigroup, regularity-preserving element, left invertive, regular left almost semigroup

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.

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Published
2020-12-25
Section
Research Articles