| 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 | 
| . |