Geodesic
Basic Algorithms for Manipulation of Modules over Finite Chain Rings
Serdica Journal of Computing, Tome 10 (2016) no. 3-4, pp. 285-297
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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.
Keywords: Chain Rings, Finitely Generated Modules over Finite Chain Rings, The Orthogonal Module, Linear Codes over Finite Chain Rings, Standard Form of a Matrix over a Chain Ring 
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     title = {Basic {Algorithms} for {Manipulation} of {Modules} over {Finite} {Chain} {Rings}},
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Georgieva, Nevyana. Basic Algorithms for Manipulation of Modules over Finite Chain Rings. Serdica Journal of Computing, Tome 10 (2016) no. 3-4, pp. 285-297. http://geodesic.mathdoc.fr/item/SJC_2016_10_3-4_a5/