Ihm-Quasiorder and Derived Structures of Universal Algebras; 1-Algebraic Complete Algebras
The relation of so-called Ihm-quasiorder (deﬁning a closure operator on subsets of direct powers of basic sets of universal algebras) with the such derived structures of these algebras as a lattices its algebraic subsets, lattices of its subalgebras, semigroups of its innere homomorphisms. We introduce the notion of 1-algebraic complete algebras and prove that for any least countinual algebra of countable signature exists its 1-algebraic complete extebsion of the same power as the algebra.