# Basic Algorithms for Manipulation of Modules over Finite Chain Rings

Serdica Journal of Computing (2016)

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

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topGeorgieva, 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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