Separability Condition in Omega Algebras

Abstract

The paper deals with Omega algebras, as an algebraic extension of Omega sets. Omega (Ω) is a complete lattice and the equality relation in an algebra is replaced by a symmetric, transitive, and compatible lattice-valued map, acting as the characteristic function of the equality and congruences on subalgebras. We aim to investigate properties of Omega algebras related to the separability condition which may be imposed on this Ω-valued map. We show that the presence or absence of this condition implies considerable various features of Ω-algebras, related mostly to the satisfiability of identities and solving the approximate equations. We also present several constructions of Ω-algebras with or without this property.