Risc Colloquium

In the first part of the talk we review main classes of difference ideals and discuss chain conditions for these classes in algebras of difference polynomials. In particular, we consider the most recent results on the ascending chain condition for mixed and mixed radical difference polynomial ideals. The second part of the presentation is devoted to the Hilbert-type dimension functions associated with prime difference polynomial ideals. We observe known results about dimension polynomials and quasi-polynomials of reflexive such ideals and then give a proof of the existence theorem for a dimension polynomial of a non-reflexive prime differential polynomial ideal in the ordinary case. In conclusion we formulate some open problems on partial difference polynomial ideals.