| Title:
|
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:
|
1275-1288 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Slim groupoids are groupoids satisfying $x(yz)\=xz$. We find all simple slim groupoids and all minimal varieties of slim groupoids. Every slim groupoid can be embedded into a subdirectly irreducible slim groupoid. The variety of slim groupoids has the finite embeddability property, so that the word problem is solvable. We introduce the notion of a strongly nonfinitely based slim groupoid (such groupoids are inherently nonfinitely based) and find all strongly nonfinitely based slim groupoids with at most four elements; up to isomorphism, there are just two such groupoids. (English) |
| Keyword:
|
groupoid |
| Keyword:
|
variety |
| Keyword:
|
nonfinitely based |
| MSC:
|
08B15 |
| MSC:
|
20N02 |
| idZBL:
|
Zbl 1161.20055 |
| idMR:
|
MR2357590 |
| . |
| Date available:
|
2009-09-24T11:52:48Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128237 |
| . |
| Reference:
|
[1] T. Evans: Embeddability and the word problem.J. London Math. Soc. 28 (1953), 76–80. Zbl 0050.02801, MR 0053915 |
| Reference:
|
[2] R. McKenzie: Tarski’s finite basis problem is undecidable.Int. J. Algebra and Computation 6 (1996), 49–104. Zbl 0844.08011, MR 1371734, 10.1142/S0218196796000040 |
| Reference:
|
[3] R. McKenzie, G. McNulty and W. Taylor: Algebras, Lattices, Varieties, Volume I.Wadsworth & Brooks/Cole, Monterey, CA, 1987. MR 0883644 |
| . |
