Subdirectly Irreducible Algebras in One Class of Algebras with One Operator and the Main Near-Unanimity Operation

In this paper we study a subdirect irreducibility of algebras with one operator and the main near-unanimity operation defined by the specific way. It is shown that congruence lattices of algebras of given class are atomic. In given class, the full description of atoms in congruence lattices of algeb...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2021, Vol.42 (1), p.206-216
Main Author: Usol’tsev, V. L.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Geometry
Lattices (mathematics)
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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Summary:In this paper we study a subdirect irreducibility of algebras with one operator and the main near-unanimity operation defined by the specific way. It is shown that congruence lattices of algebras of given class are atomic. In given class, the full description of atoms in congruence lattices of algebras, of subdirectly irreducible algebras, and of algebras with atomistic congruence lattices is obtained.
ISSN:1995-0802
1818-9962
DOI:10.1134/S199508022101025X