On semigroups of endomorphisms of universal algebras

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 2, Corollaries 7 and 8). In a free universal algebra any left ideal is a full left ideal. Theorem 1 describes the cyclic universal algebras. Theorem 3 affirms that any semigroup with unity is isomorphic to a semigroup of endomorphisms $End (G)$ of some cyclic free universal algebra $G$.