Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


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Kartashova A. V. On Congruence Lattices of Direct Sums of Strongly Connected Commutative Unary Algebras. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 4, pp. 57-62. DOI: 10.18500/1816-9791-2013-13-4-57-62

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Published online: 
25.11.2013
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On Congruence Lattices of Direct Sums of Strongly Connected Commutative Unary Algebras

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

A union of mutually disjoint unary algebras is called their direct sum. A unary algebra is said to be strongly connected if it is generated by its arbitrary element. In the present paper we investigate congruence lattices of the class of all algebras with finitely many operations whose every connected component is strongly connected. We give a necessary and sufficient condition for an algebra from this class to have a distributive congruence lattice (Theorem 1). Besides, all distributive congruence lattices of algebras from the above class are discribed (Theorem 2).      

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