Basic Algorithms for Manipulation of Modules over Finite Chain Rings

Georgieva, Nevyana

Serdica Journal of Computing (2016)

  • Volume: 10, Issue: 3-4, page 285-297
  • ISSN: 1312-6555

Abstract

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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.

How to cite

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Georgieva, Nevyana. "Basic Algorithms for Manipulation of Modules over Finite Chain Rings." Serdica Journal of Computing 10.3-4 (2016): 285-297. <http://eudml.org/doc/289531>.

@article{Georgieva2016,
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.},
author = {Georgieva, Nevyana},
journal = {Serdica Journal of Computing},
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},
language = {eng},
number = {3-4},
pages = {285-297},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Basic Algorithms for Manipulation of Modules over Finite Chain Rings},
url = {http://eudml.org/doc/289531},
volume = {10},
year = {2016},
}

TY - JOUR
AU - Georgieva, Nevyana
TI - Basic Algorithms for Manipulation of Modules over Finite Chain Rings
JO - Serdica Journal of Computing
PY - 2016
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 10
IS - 3-4
SP - 285
EP - 297
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/289531
ER -

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