Abstract
In this paper, we present some basic algorithms for manipulation of finitely generated modules over finite chain rings. We start with analgorithm that generates the standard form of a matrix over a finite chainring, which is an analogue of the row reduced echelon form for a matrix overa field. Furthermore we give an algorithm for the generation of the union oftwo modules, an algorithm for the generation of the orthogonal module to agiven module, as well as an algorithm for the generation of the intersectionof two modules. Finally, we demonstrate how to generate all submodules offixed shape of a given module.ACM Computing Classification System (1998): G.1.3, G.4.
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