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Title: Weak alg-universality and $Q$-universality of semigroup quasivarieties (English)
Author: Demlová, M.
Author: Koubek, V.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 46
Issue: 2
Year: 2005
Pages: 257-279
Category: math
Summary: In an earlier paper, the authors showed that standard semigroups $\bold M_1$, $\bold M_2$ and $\bold M_3$ play an important role in the classification of weaker versions of alg-universality of semigroup varieties. This paper shows that quasivarieties generated by $\bold M_2$ and $\bold M_3$ are neither relatively alg-universal nor $Q$-universal, while there do exist finite semigroups $\bold S_2$ and $\bold S_3$ generating the same semigroup variety as $\bold M_2$ and $\bold M_3$ respectively and the quasivarieties generated by $\bold S_2$ and/or $\bold S_3$ are quasivar-relatively $f\!f$-alg-universal and $Q$-universal (meaning that their respective lattices of subquasivarieties are quite rich). An analogous result on $Q$-universality of the variety generated by $\bold M_2$ was obtained by M.V. Sapir; the size of our semigroup is substantially smaller than that of Sapir's semigroup. (English)
Keyword: semigroup quasivariety
Keyword: full embedding
Keyword: $f\!f$-alg-universality
Keyword: $Q$-universality
MSC: 08C15
MSC: 18B15
MSC: 20M07
MSC: 20M99
idZBL: Zbl 1120.20059
idMR: MR2176891
Date available: 2009-05-05T16:50:55Z
Last updated: 2012-04-30
Stable URL:
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