|
Automorphisms of the lattice of equational theories of commutative semigroups
Author(s):
Mariusz
Grech
Journal:
Trans. Amer. Math. Soc.
361
(2009),
3435-3462.
MSC (2000):
Primary 03C07;
Secondary 03C05, 08B15
Posted:
February 23, 2009
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we complete the study of the first-order definability in the lattice of equational theories of commutative semigroups started by A. Kisielewicz in [Trans. Amer. Math. Soc. 356 (2004), 3483-3504]. We describe the group of automorphisms of this lattice and characterize first-order definable theories, thus solving the problems posed by R. McKenzie and A. Kisielewicz.
References:
-
- 1.
- M. Grech, Irreducible varieties of commutative semigroups, J. Algebra 261 (2003), 207-228. MR 1967162 (2004a:20067)
- 2.
- M. Grech, A. Kisielewicz, Covering relation for equational theories of commutative semigroups, J. Algebra 232 (2000), 493-506. MR 1792743 (2002g:20102)
- 3.
- J. Ježek, The lattice of equational theories I: Modular elements, Czech. Math. J. 31 (1981), 127-152. MR 604120 (84e:08007a)
- 4.
- J. Ježek, The lattice of equational theories II: The lattice of full sets of terms, Czech. Math. J. 31 (1982), 127-152. MR 604120 (84e:08007a)
- 5.
- J. Ježek, The lattice of equational theories III: Definability and automorphisms, Czech. Math. J. 32 (1982), 129-164. MR 646718 (84e:08007c)
- 6.
- J. Ježek, The lattice of equational theories IV: Equational theories of finite algebras, Czech. Math. J. 36 (1986), 131-141. MR 831318 (87g:08015)
- 7.
- J. Ježek, R. McKenzie, Definability in the lattice of equational theories of semigroups, Semigroup Forum 46 (1993), 199-245. MR 1200214 (94a:03052)
- 8.
- A. Kisielewicz, Varieties of commutative semigroups, Trans. Amer. Math. Soc. 342 (1994), 275-306. MR 1211411 (94j:20065)
- 9.
- A. Kisielewicz, Definability in the lattice of equational theories of commutative semigroups, Trans. Amer. Math. Soc. 356 (2004), 3483-3504. MR 2055743 (2005a:08011)
- 10.
- A. Kisielewicz, Permutability class of a semigroup, J. Algebra 226 (2000), 295-310. MR 1749890 (2001c:20122)
- 11.
- R. McKenzie, Definability in the lattice of equational theories, Annals of Math. Logic 3 (1971), 197-237. MR 0280349 (43:6069)
- 12.
- P. Perkins, Bases for equational theories of semigroups, J. Algebra 11 (1969), 298-314. MR 0233911 (38:2232)
- 13.
- A. Tarski, Equational logic and equational theories of algebras, Contributions to Mathematical Logic (Hanover 1966), 275-288, North-Holland, Amsterdam, 1968. MR 0237410 (38:5692)
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(2000):
03C07,
03C05, 08B15
Retrieve articles in all Journals with MSC
(2000):
03C07,
03C05, 08B15
Additional Information:
Mariusz
Grech
Affiliation:
Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2, 50-384 Wrocław, Poland
Email:
Mariusz.Grech@math.uni.wroc.pl
DOI:
10.1090/S0002-9947-09-04849-1
PII:
S 0002-9947(09)04849-1
Received by editor(s):
May 15, 2006
Posted:
February 23, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
|
Comments: webmaster@ams.org