On unique factorization semilattices

Pedro V. Silva

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 1, page 97-120
  • ISSN: 1509-9415

Abstract

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The class of unique factorization semilattices (UFSs) contains important examples of semilattices such as free semilattices and the semilattices of idempotents of free inverse monoids. Their structural properties allow an efficient study, among other things, of their principal ideals. A general construction of UFSs from arbitrary posets is presented and some categorical properties are derived. The problem of embedding arbitrary semilattices into UFSs is considered and complete characterizations are obtained for particular classes of semilattices. The study of the Munn semigroup for regular UFSs is developed and a complete characterization is accomplished with respect to being E-unitary.

How to cite

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Pedro V. Silva. "On unique factorization semilattices." Discussiones Mathematicae - General Algebra and Applications 20.1 (2000): 97-120. <http://eudml.org/doc/287672>.

@article{PedroV2000,
abstract = {The class of unique factorization semilattices (UFSs) contains important examples of semilattices such as free semilattices and the semilattices of idempotents of free inverse monoids. Their structural properties allow an efficient study, among other things, of their principal ideals. A general construction of UFSs from arbitrary posets is presented and some categorical properties are derived. The problem of embedding arbitrary semilattices into UFSs is considered and complete characterizations are obtained for particular classes of semilattices. The study of the Munn semigroup for regular UFSs is developed and a complete characterization is accomplished with respect to being E-unitary.},
author = {Pedro V. Silva},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {semilattice; factorization; principal ideal; semilattice embedding; Munn semigroup; prime element; connected poset; lower semilattice; meet semilattice; unique factorization semilattice; irreducible element; presentation; tree semilattice; connected semilattice; embedding; inverse semigroup},
language = {eng},
number = {1},
pages = {97-120},
title = {On unique factorization semilattices},
url = {http://eudml.org/doc/287672},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Pedro V. Silva
TI - On unique factorization semilattices
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 1
SP - 97
EP - 120
AB - The class of unique factorization semilattices (UFSs) contains important examples of semilattices such as free semilattices and the semilattices of idempotents of free inverse monoids. Their structural properties allow an efficient study, among other things, of their principal ideals. A general construction of UFSs from arbitrary posets is presented and some categorical properties are derived. The problem of embedding arbitrary semilattices into UFSs is considered and complete characterizations are obtained for particular classes of semilattices. The study of the Munn semigroup for regular UFSs is developed and a complete characterization is accomplished with respect to being E-unitary.
LA - eng
KW - semilattice; factorization; principal ideal; semilattice embedding; Munn semigroup; prime element; connected poset; lower semilattice; meet semilattice; unique factorization semilattice; irreducible element; presentation; tree semilattice; connected semilattice; embedding; inverse semigroup
UR - http://eudml.org/doc/287672
ER -

References

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  1. [1] J.M. Howie, An introduction to semigroup theory, Academic Press,London 1976. Zbl0355.20056
  2. [2] P.V. Silva, On the semilattice of idempotents of a free inverse monoid, Proc. Edinburgh Math. Soc. 36 (1993), 349-360. Zbl0796.20047

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