Basic Algorithms for Manipulation of Modules over Finite Chain Rings

Abstract

In this paper, we present some basic algorithms for manipulation of
finitely generated modules over finite chain rings. We start with an
algorithm that generates the standard form of a matrix over a finite chain
ring, which is an analogue of the row reduced echelon form for a matrix over
a field. Furthermore we give an algorithm for the generation of the union of
two modules, an algorithm for the generation of the orthogonal module to a
given module, as well as an algorithm for the generation of the intersection
of two modules. Finally, we demonstrate how to generate all submodules of
fixed shape of a given module.

ACM Computing Classification System (1998): G.1.3, G.4.