Abstract:
Recent research on the combinatorics of binomial ideals has renewed interest in congruences on commutative Noetherian monoids. Each binomial ideal in a monoid algebra defines a congruence on the monoid, and decompositions of the congruence correspond to decompositions of the binomial ideal. In 1963 primary decompositions of congruences on commutative Noetherian monoids have been described by Karel Drbohlav. As it turns out, these are not fine enough for an understanding of the combinatorics of a given binomial ideal. In this talk we discuss how to extend and adapt Drbohlav's theory such that it suits for an understanding of lattice point geometries of binomial ideals.