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Coregular semigroups of full transformations

Dimitrova I., Koppitz J.

Demonstratio Mathematica

2011

Vol. 44, nr 4

739-753

This paper is mainly dedicated to the description of coregular subsemigroups of the symmetric semigroup Tn of transformations on an n-element set. Namely, we characterize all coregular transformation semigroups S with (…). In the subsemigroup En of all extensive transformations, the coregular elements coincide with the idempotent ones. We characterize all bands within En. Within the subsemigroup OEn of all order-preserving extensive transformations, we also determine the maximal bands (with respect to the inclusion).