Title. $$\Omega$$-algebras
Speaker. Branimir Seselja
Institution. Faculty of Sciences, University of Novi Sad, Serbia
Abstract. Starting with $$\Omega$$-sets where $$\Omega$$ is a complete lattice, we introduce the notion of an $$\Omega$$-algebra. This is a classical algebra equipped with an $$\Omega$$-valued equality replacing the ordinary one. In these new structures identities hold as appropriate lattice-theoretic formulas. Our investigation is related to weak congruences of the basic algebra to which a generalized equality is associated. Namely every $$\Omega$$-algebra uniquely determines a closure system in the lattice of weak congruences of the basic algebra. By this correspondence we formulate a representation theorem for $$\Omega$$-algebras.