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

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.