Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


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Kartashov V. K., Kartashova A. V. On Conditions for Distributivity or Modularity of Congruence Lattices of Commutative Unary Algebras. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 4, pp. 52-57. DOI: 10.18500/1816-9791-2013-13-4-52-57

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.11.2013
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Russian
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On Conditions for Distributivity or Modularity of Congruence Lattices of Commutative Unary Algebras

Autors: 
Kartashov Vladimir Konstantinovich, Volgograd State Socio-pedagogical University
Kartashova Anna Vladimirovna, Volgograd State Socio-pedagogical University
Abstract: 

The paper is devoted to the problem of describing unary algebras whose congruence lattices have a given property. By now this problem has been solved for algebras with one unary operation. In the paper it is shown that this problem is much more difficult for arbitrary commutative unary algebras. We give some necessary conditions for such lattices to be distributive or modular. Besides, it is proved here that a lattice of all subsets of a set is isomorphic to the congruence lattice of a suitable connected commutative unary algebra.

References: 
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