Varieties of Distributive Rotational Lattices

Gábor Czédli; Ildikó V. Nagy

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2013)

  • Volume: 52, Issue: 1, page 71-78
  • ISSN: 0231-9721

Abstract

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A rotational lattice is a structure 〈 L ; ∨ , ∧ , g 〉 where L = 〈 L ; ∨ , ∧ 〉 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.

How to cite

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Czédli, Gábor, and Nagy, Ildikó V.. "Varieties of Distributive Rotational Lattices." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 52.1 (2013): 71-78. <http://eudml.org/doc/260631>.

@article{Czédli2013,
abstract = {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.},
author = {Czédli, Gábor, Nagy, Ildikó V.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {rotational lattice; lattice with automorphism; lattice with involution; distributivity; lattice variety; rotational lattices; lattices with automorphisms; lattices with involution; distributivity; lattice varieties; subdirectly irreducible distributive lattices},
language = {eng},
number = {1},
pages = {71-78},
publisher = {Palacký University Olomouc},
title = {Varieties of Distributive Rotational Lattices},
url = {http://eudml.org/doc/260631},
volume = {52},
year = {2013},
}

TY - JOUR
AU - Czédli, Gábor
AU - Nagy, Ildikó V.
TI - Varieties of Distributive Rotational Lattices
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2013
PB - Palacký University Olomouc
VL - 52
IS - 1
SP - 71
EP - 78
AB - 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.
LA - eng
KW - rotational lattice; lattice with automorphism; lattice with involution; distributivity; lattice variety; rotational lattices; lattices with automorphisms; lattices with involution; distributivity; lattice varieties; subdirectly irreducible distributive lattices
UR - http://eudml.org/doc/260631
ER -

References

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  3. Chajda, I., Czédli, G., Halaš, R., 10.1007/s00012-012-0213-0, Algebra Universalis 69 (2013), 83–92. (2013) MR3029971DOI10.1007/s00012-012-0213-0
  4. Czédli, G., Szabó, L., Quasiorders of lattices versus pairs of congruences, Acta Sci. Math. (Szeged) 60 (1995), 207–211. (1995) Zbl0829.06008MR1348689
  5. Dziobiak, W., Ježek, J., Maróti, M., 10.1007/s00233-008-9087-z, Semigroup Forum 78 (2009), 253–261. (2009) Zbl1171.08002MR2486638DOI10.1007/s00233-008-9087-z
  6. Grätzer, G.:, Lattice Theory: Foundation, Birkhäuser Verlag, Basel, 2011. (2011) Zbl1233.06001MR2768581
  7. Ježek, J., 10.1007/BF02574263, Semigroup Forum 43 (1991), 178–186. (1991) Zbl0770.08004MR1114689DOI10.1007/BF02574263
  8. Jónsson, B., Algebras whose congruence lattices are distributive, Math. Scand. 21 (1967), 110–121. (1967) MR0237402
  9. Maróti, M., 10.1007/s000120050054, Algebra Universalis 38 (1997), 238–265. (1997) MR1619766DOI10.1007/s000120050054
  10. Nagy, I. V., Minimal quasivarieties of semilattices over commutative groups, Algebra Universalis (to appear). 
  11. Vetterlein, T., Boolean algebras with an automorphism group: a framework for Łukasiewicz logic, J. Mult.-Val. Log. Soft Comput. 14 (2008), 51–67. (2008) Zbl1236.03018MR2456707

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