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On sandwich sets and congruences on regular semigroups

Mario Petrich (2006)

Czechoslovak Mathematical Journal

Let S be a regular semigroup and E ( S ) be the set of its idempotents. We call the sets S ( e , f ) f and e S ( e , f ) one-sided sandwich sets and characterize them abstractly where e , f E ( S ) . For a , a ' S such that a = a a ' a , a ' = a ' a a ' , we call S ( a ) = S ( a ' a , a a ' ) the sandwich set of a . We characterize regular semigroups S in which all S ( e , f ) (or all S ( a ) ) are right zero semigroups (respectively are trivial) in several ways including weak versions of compatibility of the natural order. For every a S , we also define E ( a ) as the set of all idempotets e such that, for any congruence ρ on...

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