On unars with identities in congruence lattice, II

I. B. Kozhukhov^abc, A. M. Pryanichnikov<sup>cd

a</sup> The Russian Presidential Academy of National Economy and Public Administration (Moscow)
^b National Research University MIET (Moscow)
^c Lomonosov Moscow State University (Moscow)
^d «Kvantom» LLC (Moscow)

Abstract: We prove that if a congruence lattice of a unar satisfies a non-trivial lattice identity, then the unar is a homomorphic image of a coproduct of finite number of lines and rays, which, in turn, is equivalent to the fact that the unar has only a finite number of connected components, knots, initial elements, and input degree of each element of the unar is finite.

Keywords: act over semigroup, unar, congruence lattice, identity.

UDC: 512.567.5 + 512.579

Received: 19.05.2025
Revised: 27.08.2025

DOI: 10.22405/2226-8383-2025-26-3-125-135