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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1188,
author = {Prakit Jampachon and Yeni Susanti and Klaus Denecke},
title = {Four-part semigroups - semigroups of Boolean operations},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {32},
year = {2012},
pages = {115-136},
zbl = {1305.08003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1188}
}
Prakit Jampachon; Yeni Susanti; Klaus Denecke. Four-part semigroups - semigroups of Boolean operations. Discussiones Mathematicae - General Algebra and Applications, Tome 32 (2012) pp. 115-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1188/
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