"A Normal Form Algorithm for Matrices over k[x,y]/<xy>".
  Reinhard Laubenbacher
  rlaubenb@nmsu.edu


Reinhard Laubenbacher
New Mexico State University
Department of Mathematical Sciences
Las Cruces, NM 88003-0001 USA


ABSTRACT: The classification of finitely generated modules over a principal
ideal domain is one of the fundamental results of algebra.  Every such module
can be written uniquely, up to order of summands, as a direct sum of
indecomposable modules which are either copies of the ring or are quotients of
the ring modulo a power of a prime ideal.  If the module is presented as the
cokernel of a matrix then one can find this decomposition by computing the
Smith normal form of the matrix.  In this talk the Smith normal form algorithm
is generalized to the ring  k[x,y]/<xy>  of polynomials in  x  and y  without
mixed terms.

As an application one obtains an algorithmic classification of finitely
generated modules over  k[x,y]/<xy>, and related rings such as certain types
of group rings.  Looking at the problem from a different point of view, one
obtains an algorithmic classification of pairs of mutually annihilating linear
operators on a finite dimensional vector space.