Congruences associated with inverse transversals.
T. S. Blyth, M. H. Almeida Santos · RACO (Revistes Catalanes amb Accés Obert) (Consorci de Serveis Universitaris de Catalunya) · 1995
An inverse transversal of a regular semigroup $S$ is an inverse subsemigroup of $S$ that contains a unique inverse $x^\circ$ of every element $x$ of $S$. Here we consider the congruences on such a semigroup, considered as an algebra of type (2, 1). The structure of such semigroups being known, with 'building bricks' the inverse subsemigroup $S^\circ$ and the sub-bands $I = \{xx^\circ; x\in S\},\Lambda = \{x^\circ x; x\in S\}$, we investigate how congruences on $S$ are related to congruences on these building bricks.