Previous |  Up |  Next

Article

Title: Varieties of Distributive Rotational Lattices (English)
Author: Czédli, Gábor
Author: Nagy, Ildikó V.
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 52
Issue: 1
Year: 2013
Pages: 71-78
Summary lang: English
.
Category: math
.
Summary: A rotational lattice is a structure $\langle L;\vee ,\wedge , g\rangle $ where $L=\langle L;\vee ,\wedge \rangle $ is a lattice and $g$ is a lattice automorphism of finite order. We describe the subdirectly irreducible distributive rotational lattices. Using Jónsson’s lemma, this leads to a description of all varieties of distributive rotational lattices. (English)
Keyword: rotational lattice
Keyword: lattice with automorphism
Keyword: lattice with involution
Keyword: distributivity
Keyword: lattice variety
MSC: 06B20
MSC: 06B75
MSC: 06D99
idZBL: Zbl 06285755
idMR: MR3202750
.
Date available: 2013-08-02T07:58:39Z
Last updated: 2014-07-30
Stable URL: http://hdl.handle.net/10338.dmlcz/143392
.
Reference: [1] Burris, S., Sankappanavar, H. P.: A Course in Universal Algebra. Graduate Texts in Mathematics 78, Springer-Verlag, New York–Berlin, 1981. The Millennium Edition: http://www.math.uwaterloo.ca/s̃nburris/htdocs/ualg.html. Zbl 0478.08001, MR 0648287
Reference: [2] Chajda, I., Czédli, G: How to generate the involution lattice of quasiorders?. Studia Sci. Math. Hungar. 32 (1996), 415–427. Zbl 0864.06003, MR 1432183
Reference: [3] Chajda, I., Czédli, G., Halaš, R.: Independent joins of tolerance factorable varieties. Algebra Universalis 69 (2013), 83–92. MR 3029971, 10.1007/s00012-012-0213-0
Reference: [4] Czédli, G., Szabó, L.: Quasiorders of lattices versus pairs of congruences. Acta Sci. Math. (Szeged) 60 (1995), 207–211. Zbl 0829.06008, MR 1348689
Reference: [5] Dziobiak, W., Ježek, J., Maróti, M.: Minimal varieties and quasivarieties of semilattices with one automorphism. Semigroup Forum 78 (2009), 253–261. Zbl 1171.08002, MR 2486638, 10.1007/s00233-008-9087-z
Reference: [6] Grätzer, G.:: Lattice Theory: Foundation. Birkhäuser Verlag, Basel, 2011. Zbl 1233.06001, MR 2768581
Reference: [7] Ježek, J.: Subdirectly irreducible semilattices with an automorphism. Semigroup Forum 43 (1991), 178–186. Zbl 0770.08004, MR 1114689, 10.1007/BF02574263
Reference: [8] Jónsson, B.: Algebras whose congruence lattices are distributive. Math. Scand. 21 (1967), 110–121. MR 0237402
Reference: [9] Maróti, M.: Semilattices with a group of automorphisms. Algebra Universalis 38 (1997), 238–265. MR 1619766, 10.1007/s000120050054
Reference: [10] Nagy, I. V.: Minimal quasivarieties of semilattices over commutative groups. Algebra Universalis (to appear).
Reference: [11] Vetterlein, T.: Boolean algebras with an automorphism group: a framework for Łukasiewicz logic. J. Mult.-Val. Log. Soft Comput. 14 (2008), 51–67. Zbl 1236.03018, MR 2456707
.

Files

Files Size Format View
ActaOlom_52-2013-1_6.pdf 240.9Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo