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

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Abstract

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.

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ACKNOWLEDGMENTS

The author thanks the anonymous referee for correcting the English and for his constructive comments and suggestions, which have significantly contributed to improving the quality of the paper.

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  1. Volgograd State Socio-Pedagogical University, 400066, Volgograd, Russia

    V. L. Usol’tsev

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  1. V. L. Usol’tsev
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Correspondence to V. L. Usol’tsev.

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(Submitted byM. M. Arslanov)

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Usol’tsev, V.L. Subdirectly Irreducible Algebras in One Class of Algebras with One Operator and the Main Near-Unanimity Operation. Lobachevskii J Math 42, 206–216 (2021). https://doi.org/10.1134/S199508022101025X

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  • DOI: https://doi.org/10.1134/S199508022101025X

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