Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2929

 Title: Basic Algorithms for Manipulation of Modules over Finite Chain Rings Authors: Georgieva, Nevyana Keywords: Chain RingsFinitely Generated Modules over Finite Chain RingsThe Orthogonal ModuleLinear Codes over Finite Chain RingsStandard Form of a Matrix over a Chain Ring Issue Date: 2016 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Journal of Computing, Vol. 10, No 3-4, (2016), 285p-297p 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. URI: http://hdl.handle.net/10525/2929 ISSN: 1312-6555 Appears in Collections: Volume 10 Number 3-4

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