| 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:
|
http://hdl.handle.net/10338.dmlcz/119523 |
| . |
| Reference:
|
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| . |
