# Four-part semigroups - semigroups of Boolean operations

Prakit Jampachon; Yeni Susanti; Klaus Denecke

Discussiones Mathematicae - General Algebra and Applications (2012)

- Volume: 32, Issue: 1, page 115-136
- ISSN: 1509-9415

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topPrakit 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 -

## References

top- [1] R. Butkote and K. Denecke, Semigroup Properties of Boolean Operations, Asian-Eur. J. Math. 1 (2008) 157-176. Zbl1176.20060
- [2] R. Butkote, Universal-algebraic and Semigroup-theoretical Properties of Boolean Operations (Dissertation Universität Potsdam, 2009).

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