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IMI/Publicaţii/BASM/Ediţii/BASM n.3(94), 2020/

On semigroups of endomorphisms of universal algebras

Authors: Mitrofan M. Choban, Ion I. Valuţă

Abstract

In the present article the left ideals of the semigroup of endomorphisms $End (G)$ of a universal algebra $G$ are studied. The lattice $Spec^s(G)$ of saturated left ideals and the lattice $Spec^f(G)$ of full ideals of the semigroup of endomorphisms $End (G)$ of a universal algebra $G$ are introduced and characterized (Theorem \ref{T3.2}, Corollaries \ref{C.5.1} and \ref{C.5.2}). In a free universal algebra any left ideal is a full left ideal. Theorem \ref{T3.1} describes the cyclic universal algebras. Theorem \ref{T4.1} affirms that any semigroup with unity is isomorphic to a semigroup of endomorphisms $End (G)$ of some cyclic free universal algebra $G$.

Department of Mathematics, Technical University of
Moldova, Chisinau, Republic of Moldova

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