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Andreja Tepavcevic (University of Novi Sad and MI SANU Belgrade): Weak congruences, closure systems and latticevalued structures 



Wednesday, 20. February 2019, 10:00  12:00


Abstract. Starting with Ωsets where Ω is a complete lattice, we introduce the notion of an Ωalgebra, which is a classical algebra equipped with an Ωvalued equality replacing the ordinary one. In these new structures identities hold as appropriate latticetheoretic formulas. Identities hold in such an algebra if and only if they hold on all particular cutfactor algebras, i.e., cut subalgebras over cutequalities. This approach is directly related to weak congruences of the basic algebra to which a generalized equality is associated. Namely every Ωalgebra uniquely determines a closure system in the lattice of weak congruences of the basic algebra. By this correspondence we formulate a representation theorem for Ωalgebras. 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. 
Location : Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged 
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