| Title:
|
The ordering of commutative terms (English) |
| Author:
|
Ježek, J. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
133-154 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By a commutative term we mean an element of the free commutative groupoid $F$ of infinite rank. For two commutative terms $a$, $b$ write $a\le b$ if $b$ contains a subterm that is a substitution instance of $a$. With respect to this relation, $F$ is a quasiordered set which becomes an ordered set after the appropriate factorization. We study definability in this ordered set. Among other things, we prove that every commutative term (or its block in the factor) is a definable element. Consequently, the ordered set has no automorphisms except the identity. (English) |
| Keyword:
|
definable |
| Keyword:
|
term |
| MSC:
|
03C40 |
| MSC:
|
06A07 |
| MSC:
|
08B20 |
| idZBL:
|
Zbl 1164.03318 |
| idMR:
|
MR2207011 |
| . |
| Date available:
|
2009-09-24T11:32:04Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128058 |
| . |
| Reference:
|
[1] J. Ježek: The lattice of equational theories. Part I: Modular elements.Czechoslovak Math. J. 31 (1981), 127–152. MR 0604120 |
| Reference:
|
[2] J. Ježek: The lattice of equational theories. Part II: The lattice of full sets of terms.Czechoslovak Math. J. 31 (1981), 573–603. MR 0631604 |
| Reference:
|
[3] J. Ježek: The lattice of equational theories. Part III: Definability and automorphisms.Czechoslovak Math. J. 32 (1982), 129–164. MR 0646718 |
| Reference:
|
[4] J. Ježek: The lattice of equational theories. Part IV: Equational theories of finite algebras.Czechoslovak Math. J. 36 (1986), 331–341. MR 0831318 |
| Reference:
|
[5] J. Ježek and R. McKenzie: Definability in the lattice of equational theories of semigroups.Semigroup Forum 46 (1993), 199–245. MR 1200214 |
| Reference:
|
[6] A. Kisielewicz: Definability in the lattice of equational theories of commutative semigroups.Trans. Amer. Math. Soc. 356 (2004), 3483–3504. Zbl 1050.08005, MR 2055743, 10.1090/S0002-9947-03-03351-8 |
| Reference:
|
[7] R. McKenzie, G. McNulty and W. Taylor: Algebras, Lattices, Varieties, Volume I.Wadsworth & Brooks/Cole, Monterey, CA, 1987. MR 0883644 |
| . |
