| Title:
|
Varieties of idempotent slim groupoids (English) |
| Author:
|
Ježek, J. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
1289-1309 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Idempotent slim groupoids are groupoids satisfying $xx\=x$ and $x(yz)\=xz$. We prove that the variety of idempotent slim groupoids has uncountably many subvarieties. We find a four-element, inherently nonfinitely based idempotent slim groupoid; the variety generated by this groupoid has only finitely many subvarieties. We investigate free objects in some varieties of idempotent slim groupoids determined by permutational equations. (English) |
| Keyword:
|
groupoid |
| Keyword:
|
variety |
| Keyword:
|
nonfinitely based |
| MSC:
|
08B15 |
| MSC:
|
20N02 |
| idZBL:
|
Zbl 1161.20056 |
| idMR:
|
MR2357591 |
| . |
| Date available:
|
2009-09-24T11:52:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128238 |
| . |
| Reference:
|
[1] S. Crvenković and J. Dudek: Rectangular groupoids.Czech. Math. J. 35 (1985), 405–414. MR 0803035 |
| Reference:
|
[2] J. A. Gerhard: The lattice of equational classes of idempotent semigroups.J. Algebra 15 (1970), 195–224. Zbl 0194.02701, MR 0263953, 10.1016/0021-8693(70)90073-6 |
| Reference:
|
[3] E. Jacobs and R. Schwabauer: The lattice of equational classes of algebras with one unary operation.Ann. of Math. 71 (1964), 151–155. MR 0162740 |
| Reference:
|
[4] J. Ježek: Slim groupoids.(to appear). MR 2357590 |
| Reference:
|
[5] R. McKenzie, G. McNulty and W. Taylor: Algebras, Lattices, Varieties, Volume I.Wadsworth & Brooks/Cole, Monterey, CA, 1987. MR 0883644 |
| . |
