Rings of matrix invariants in positive characteristic

Computing Invariants of Reductive Groups in Positive Characteristic

This paper gives an algorithm for computing invariant rings of reductive groups in arbitrary characteristic. Previously, only algorithms for linearly reductive groups and for finite groups have been known. The key step is to find a separating set of invariants.

Differential Polynomial Rings of Triangular Matrix Rings

Uniform Positive Existential Interpretation of the Integers in Rings of Entire Functions of Positive Characteristic

We prove a negative solution to the analogue of Hilbert’s tenth problem for rings of one variable non-Archimedean entire functions in any characteristic. In the positive characteristic case we prove more: the ring of rational integers is uniformly positive existentially interpretable in the class of {0, 1, t,+, ·,=}-structures consisting of positive characteristic rings of entire functions on t...

Invariants of Group Rings

Since the foundation paper of M. Auslander and 0. Goldman [ 1 J, several authors have generalized constructions for studying group algebras over fields to separable algebras over commutative rings. Specifically, we have in mind the Schur index [20], the Schur exponent [18], the Schur group [S], and the uniform group [ 111. This paper gives additional properties of these constructions and studie...

Deciding finiteness of matrix groups in positive characteristic

Article history: Received 29 June 2009 Available online 1 October 2009 Communicated by Derek Holt