Four-part semigroups - semigroups of Boolean operations

Prakit Jampachon, Yeni Susanti, and Klaus Denecke. "Four-part semigroups - semigroups of Boolean operations." Discussiones Mathematicae - General Algebra and Applications 32.1 (2012): 115-136. <http://eudml.org/doc/270591>.

@article{PrakitJampachon2012,
abstract = {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.},
author = {Prakit Jampachon, Yeni Susanti, Klaus Denecke},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {four-part semigroup; Boolean operation; four-part semigroups; Boolean operations; regular semigroups; clones; idempotents; Green relations; finitary operations; regular elements},
language = {eng},
number = {1},
pages = {115-136},
title = {Four-part semigroups - semigroups of Boolean operations},
url = {http://eudml.org/doc/270591},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Prakit Jampachon
AU - Yeni Susanti
AU - Klaus Denecke
TI - Four-part semigroups - semigroups of Boolean operations
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2012
VL - 32
IS - 1
SP - 115
EP - 136
AB - 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.
LA - eng
KW - four-part semigroup; Boolean operation; four-part semigroups; Boolean operations; regular semigroups; clones; idempotents; Green relations; finitary operations; regular elements
UR - http://eudml.org/doc/270591
ER -