| Title:
|
Commutative idempotent residuated lattices (English) |
| Author:
|
Stanovský, David |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
191-200 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the variety of residuated lattices with a commutative and idempotent monoid reduct. (English) |
| Keyword:
|
residuated lattice |
| Keyword:
|
semilattice |
| Keyword:
|
finitely based variety |
| Keyword:
|
minimal variety |
| MSC:
|
06B20 |
| MSC:
|
06F05 |
| idZBL:
|
Zbl 1174.06332 |
| idMR:
|
MR2309960 |
| . |
| Date available:
|
2009-09-24T11:45:06Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128166 |
| . |
| Reference:
|
[1] P. Bahls, J. Cole, N. Galatos, P. Jipsen, and C. Tsinakis: Cancellative residuated lattices.Algebra Universalis 50 (2003), 83–106. MR 2026830, 10.1007/s00012-003-1822-4 |
| Reference:
|
[2] K. Baker, J. Wang: Definable principal subcongruences.Algebra Universalis 47 (2002), 145–151. MR 1916612, 10.1007/s00012-002-8180-5 |
| Reference:
|
[3] S. Burris, H. P. Sankappanavar: A Course in Universal Algebra. GTM 78.Springer-Verlag, New York-Heidelberg-Berlin, 1981. MR 0648287 |
| Reference:
|
[4] K. Blount, C. Tsinakis: The structure of residuated lattices.Internat. J. Algebra Comput. 13 (2003), 437–461. MR 2022118, 10.1142/S0218196703001511 |
| Reference:
|
[5] R. P. Dilworth, M. Ward: Residuated lattices.Trans. Amer. Math. Soc. 45 (1939), 335–354. MR 1501995, 10.1090/S0002-9947-1939-1501995-3 |
| Reference:
|
[6] N. Galatos: Minimal varieties of residuated-lattices.Algebra Universalis 52 (2004), 215–239. Zbl 1082.06011, MR 2161651, 10.1007/s00012-004-1870-4 |
| Reference:
|
[7] N. Galatos: Equational bases for joins of residuated-lattice varieties.Studia Logica 76 (2004), 227–240. Zbl 1068.06007, MR 2072984, 10.1023/B:STUD.0000032086.42963.7c |
| Reference:
|
[8] N. Galatos: Varieties of residuated lattices.PhD. Thesis, Vanderbilt University, 2003. MR 2704503 |
| Reference:
|
[9] J. Hart, L. Rafter, and C. Tsinakis: The structure of commutative residuated lattices.Internat. J. Algebra Comput. 12 (2002), 509–524. MR 1919685, 10.1142/S0218196702001048 |
| Reference:
|
[10] P. Jipsen, C. Tsinakis: A survey of residuated lattices.In: Ordered Algebraic Structures, J. Martinez (ed.), Kluwer Academic Publishers, Dordrecht, 2002, pp. 19–56. MR 2083033 |
| Reference:
|
[11] R. McKenzie: Equational bases for lattice theories.Math. Scand. 27 (1970), 24–38. Zbl 0307.08001, MR 0274353, 10.7146/math.scand.a-10984 |
| Reference:
|
[12] R. McKenzie, G. McNulty, and W. Taylor: Algebras, Lattices, Varieties, Vol I.Wadsworth & Brooks/Cole, Monterey, 1987. MR 0883644 |
| . |
