On categorical equivalence of finite arithmetical algebras

Abstract:
In the talk we try to give a characterization up to equivalence of finite algebras which 1) do not have proper subalgebras, 2) do not have different isomorphic quotient algebras, and 3) generate an arithmetical variety. In the first talk, the notion of categorical equivalence is presented together with general results about it, including C. Bergman's result, which concerns algebras having majority term. After that we consider abovementioned special cases and show that these algebras are categorically equivalent if and only if their so called group schemes are isomorphic.