A multiplication of e -varieties of orthodox semigroups

Martin Kuřil

Archivum Mathematicum (1995)

  • Volume: 031, Issue: 1, page 43-54
  • ISSN: 0044-8753

Abstract

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We define semantically a partial multiplication on the lattice of all e–varieties of regular semigroups. In the case that the first factor is an e–variety of orthodox semigroups we describe our multiplication syntactically in terms of biinvariant congruences.

How to cite

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Kuřil, Martin. "A multiplication of $e$-varieties of orthodox semigroups." Archivum Mathematicum 031.1 (1995): 43-54. <http://eudml.org/doc/247679>.

@article{Kuřil1995,
abstract = {We define semantically a partial multiplication on the lattice of all e–varieties of regular semigroups. In the case that the first factor is an e–variety of orthodox semigroups we describe our multiplication syntactically in terms of biinvariant congruences.},
author = {Kuřil, Martin},
journal = {Archivum Mathematicum},
keywords = {regular semigroup; orthodox semigroup; inverse semigroup; e–variety; biinvariant congruence; existence variety; orthodox semigroups; partial binary operations; lattice of e-varieties of regular semigroups; inverse semigroups; -semidirect products; bifree objects},
language = {eng},
number = {1},
pages = {43-54},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A multiplication of $e$-varieties of orthodox semigroups},
url = {http://eudml.org/doc/247679},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Kuřil, Martin
TI - A multiplication of $e$-varieties of orthodox semigroups
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 1
SP - 43
EP - 54
AB - We define semantically a partial multiplication on the lattice of all e–varieties of regular semigroups. In the case that the first factor is an e–variety of orthodox semigroups we describe our multiplication syntactically in terms of biinvariant congruences.
LA - eng
KW - regular semigroup; orthodox semigroup; inverse semigroup; e–variety; biinvariant congruence; existence variety; orthodox semigroups; partial binary operations; lattice of e-varieties of regular semigroups; inverse semigroups; -semidirect products; bifree objects
UR - http://eudml.org/doc/247679
ER -

References

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  1. Congruences and Green’s relations on regular semigroups, Glasgow Math. J. 13 (1972), 167-175. (1972) MR0318356
  2. Identities for existence varieties of regular semigroups, Bull. Austral. Math. Soc. 40 (1989), 59-77. (1989) Zbl0666.20028MR1020841
  3. An Introduction to Semigroup Theory, Academic Press, London, 1976. Zbl0355.20056MR0466355
  4. A new approach in the theory of orthodox semigroups, Semigroup Forum 40 (1990), 257-296. (1990) MR1038007
  5. A multiplication on the lattice of varieties of * -regular semigroups, to appear in Proceedings of Luino International Conference on Semigroups. 

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