| Title:
|
Definability for equational theories of commutative groupoids (English) |
| Author:
|
Ježek, Jaroslav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
305-333 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We find several large classes of equations with the property that every automorphism of the lattice of equational theories of commutative groupoids fixes any equational theory generated by such equations, and every equational theory generated by finitely many such equations is a definable element of the lattice. We conjecture that the lattice has no non-identical automorphisms. (English) |
| Keyword:
|
simple algebra |
| Keyword:
|
idempotent |
| Keyword:
|
group |
| MSC:
|
08A35 |
| MSC:
|
08B15 |
| MSC:
|
08B26 |
| MSC:
|
20N02 |
| idZBL:
|
Zbl 1265.08013 |
| idMR:
|
MR2990179 |
| DOI:
|
10.1007/s10587-012-0032-7 |
| . |
| Date available:
|
2012-06-08T09:35:21Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142831 |
| . |
| Reference:
|
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| Reference:
|
[2] Grech, M.: Automorphism of the lattice of equational theories of commutative semigroups.Trans. Am. Math. Soc. 361 (2009), 3435-3462. MR 2491887, 10.1090/S0002-9947-09-04849-1 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Ježek, J., McKenzie, R.: Definability in the lattice of equational theories of semigroups.Semigroup Forum 46 (1993), 199-245. Zbl 0782.20051, MR 1200214, 10.1007/BF02573566 |
| Reference:
|
[9] Kisielewicz, A.: Definability in the lattice of equational theories of commutative semigroups.Trans. Am. Math. Soc. 356 (2004), 3483-3504. Zbl 1050.08005, MR 2055743, 10.1090/S0002-9947-03-03351-8 |
| Reference:
|
[10] McKenzie, R. N., McNulty, G. F., Taylor, W. F.: Algebras, Lattices, Varieties. Volume I.Wadsworth & Brooks/Cole Monterey (1987). Zbl 0611.08001, MR 0883644 |
| Reference:
|
[11] Tarski, A.: Equational logic and equational theories of algebras. Proc. Logic Colloq., Hannover 1966.Contrib. Math. Logic (1968), 275-288. MR 0237410 |
| Reference:
|
[12] Vernikov, B. M.: Proofs of definability of some varieties and sets of varieties of semigroups.Preprint. MR 2898768 |
| . |
