Abstract
By an associate inverse subsemigroup of a regular semigroup S we mean a subsemigroup T of S containing a least associate of each x∈S, in relation to the natural partial order ≤ S . We describe the structure of a regular semigroup with an associate inverse subsemigroup, satisfying two natural conditions. As a particular application, we obtain the structure of regular semigroups with an associate subgroup with medial identity element.
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