Lattice-theoretically characterized classes of finite bands

Reinhard Thron; Jörg Koppitz

Archivum Mathematicum (2003)

  • Volume: 039, Issue: 1, page 1-10
  • ISSN: 0044-8753

Abstract

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There are investigated classes of finite bands such that their subsemigroup lattices satisfy certain lattice-theoretical properties which are related with the cardinalities of the Green’s classes of the considered bands, too. Mainly, there are given disjunctions of equations which define the classes of finite bands.

How to cite

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Thron, Reinhard, and Koppitz, Jörg. "Lattice-theoretically characterized classes of finite bands." Archivum Mathematicum 039.1 (2003): 1-10. <http://eudml.org/doc/249145>.

@article{Thron2003,
abstract = {There are investigated classes of finite bands such that their subsemigroup lattices satisfy certain lattice-theoretical properties which are related with the cardinalities of the Green’s classes of the considered bands, too. Mainly, there are given disjunctions of equations which define the classes of finite bands.},
author = {Thron, Reinhard, Koppitz, Jörg},
journal = {Archivum Mathematicum},
keywords = {subsemigroup lattices; finite bands; subsemigroup lattices; classes of finite bands; lattices of subsemigroups; equational classes},
language = {eng},
number = {1},
pages = {1-10},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Lattice-theoretically characterized classes of finite bands},
url = {http://eudml.org/doc/249145},
volume = {039},
year = {2003},
}

TY - JOUR
AU - Thron, Reinhard
AU - Koppitz, Jörg
TI - Lattice-theoretically characterized classes of finite bands
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 1
SP - 1
EP - 10
AB - There are investigated classes of finite bands such that their subsemigroup lattices satisfy certain lattice-theoretical properties which are related with the cardinalities of the Green’s classes of the considered bands, too. Mainly, there are given disjunctions of equations which define the classes of finite bands.
LA - eng
KW - subsemigroup lattices; finite bands; subsemigroup lattices; classes of finite bands; lattices of subsemigroups; equational classes
UR - http://eudml.org/doc/249145
ER -

References

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  1. Meet-distributive lattices and the anti-exchange closure, Algebra Universalis 10 (1980), 290–299. (1980) Zbl0442.06004MR0564118
  2. Semigroups with some power identity inclusions, Algebraic systems with one operation and one relation, Interuniv. Collect. sci. Works, Leningrad 1985, 21–32. (Russian) MR0855648
  3. General lattice theory, Birkhäuser Verlag Basel und Stuttgart 1978. MR0504338
  4. A construction and a classification of bands, Math. Nachr. 48 (1971), 263–274. (1971) Zbl0194.02702MR0294542
  5. Finite filtered semigroups, Mat. Sb. 182, no. 9 (1991), 1331–1356. (Russian) (1991) MR1133573
  6. Filtered semigroups, Mat. Zap. 14, no. 1 (1985), 171–184. (Russian) (1985) Zbl0644.20035MR0867386

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