Endre Tóth (SZTE): Solution sets of systems of equations over finite algebras

 Wednesday, 28. November 2018, 10:00 - 12:00
Abstract. Solution sets of systems of homogeneous linear equations over fields are characterized as being subspaces. But what can we say about the “shape” of the set of all solutions of other systems of equations? We study solution sets over arbitrary algebraic structures, and we give a necessary condition for a set of n-tuples to be the set of solutions of a system of equations in n unknowns over a given algebra. If the condition is sufficient as well, then we will talk about (the given algebra having) Property (SSCC). In the case of Boolean equations we obtain a complete characterization, and we also characterize lattices and semilattices having Property (SSCC).
Location : Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged