### Two Congruence Lattices of Completely Simple Semigroups.

Mario Petrich (1993)

Monatshefte für Mathematik

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Mario Petrich (1993)

Monatshefte für Mathematik

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Monatshefte für Mathematik

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K. Auinger (1991)

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Prakit Jampachon, Yeni Susanti, Klaus Denecke (2012)

Discussiones Mathematicae - General Algebra and Applications

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Four-part semigroups form a new class of semigroups which became important when sets of Boolean operations which are closed under the binary superposition operation f + g := f(g,...,g), were studied. In this paper we describe the lattice of all subsemigroups of an arbitrary four-part semigroup, determine regular and idempotent elements, regular and idempotent subsemigroups, homomorphic images, Green's relations, and prove a representation theorem for four-part semigroups.

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