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.
@article{107849,
author = {Reinhard Thron and J\"org Koppitz},
title = {Lattice-theoretically characterized classes of finite bands},
journal = {Archivum Mathematicum},
volume = {039},
year = {2003},
pages = {1-10},
zbl = {1114.20035},
mrnumber = {1982207},
language = {en},
url = {http://dml.mathdoc.fr/item/107849}
}
Thron, Reinhard; Koppitz, Jörg. Lattice-theoretically characterized classes of finite bands. Archivum Mathematicum, Tome 039 (2003) pp. 1-10. http://gdmltest.u-ga.fr/item/107849/
Meet-distributive lattices and the anti-exchange closure, Algebra Universalis 10 (1980), 290–299. (1980) | MR 0564118 | Zbl 0442.06004
Semigroups with some power identity inclusions, Algebraic systems with one operation and one relation, Interuniv. Collect. sci. Works, Leningrad 1985, 21–32. (Russian) | MR 0855648
General lattice theory, Birkhäuser Verlag Basel und Stuttgart 1978. | MR 0504338
A construction and a classification of bands, Math. Nachr. 48 (1971), 263–274. (1971) | MR 0294542 | Zbl 0194.02702
Finite filtered semigroups, Mat. Sb. 182, no. 9 (1991), 1331–1356. (Russian) (1991) | MR 1133573
Filtered semigroups, Mat. Zap. 14, no. 1 (1985), 171–184. (Russian) (1985) | MR 0867386 | Zbl 0644.20035