Leírás
University of Szeged, Bolyai Institute, Algebra Seminar
Abstract. Starting with Ω-sets where Ω is a complete lattice, we introduce the notion of an Ω-algebra, which is a classical algebra equipped with an Ω-valued equality replacing the ordinary one. In these new structures identities hold as appropriate lattice-theoretic formulas. Identities hold in such an algebra if and only if they hold on all particular cut-factor algebras, i.e., cut subalgebras over cut-equalities. This approach is directly related to weak congruences of the basic algebra to which a generalized equality is associated. Namely every Ω-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 Ω-algebras. Some special classes of such algebras will be elaborated as well as approach to varieties of such algebras.
This is a join work with Branimir Seselja.