ALH-2018

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.