On the equivalence of types

Types over a discrete valued field $(K,v)$ are computational objects that parameterize certain families of monic irreducible polynomials in $K_v[x]$, where $K_v$ is the completion of $K$ at $v$. Two types are considered to be equivalent if they encode the same family of prime polynomials. In this paper, we characterize the equivalence of types in terms of certain data supported by them

Similarity classes of 3x3 matrices over a local principal ideal ring

In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.Comment: 14 pages, final version, to appear in Communications in Algebr

On Representations of General Linear Groups over Principal Ideal Local Rings of Length Two

We study the irreducible complex representations of general linear groups over principal ideal local rings of length two with a fixed finite residue field. We construct a canonical correspondence between the irreducible representations of all such groups which preserves dimensions. For general linear groups of order three and four over these rings, we construct all the irreducible representations. We show that the the problem of constructing all the irreducible representations of all general linear groups over these rings is not easier than the problem of constructing all the irreducible representations of the general linear groups over principal ideal local rings of arbitrary length in the function field case.Comment: 21 page