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Ihm-quasiorder and derived structures of universal algebras; 1-algebraic complete algebras

A. G. Pinus

Novosibirsk State Technical University, 20, K. Marx pr., Novosibirsk, 630073

Abstract: 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.

Keywords: Ihm-quasiorder, algebraic sets, innere homomorphisms, 1-algebraic complete algebras.

UDC: 512.57