Geodesic
Classification of finite rings: theory and algorithm
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 641-658 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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An interesting topic in the ring theory is the classification of finite rings. Although rings of certain orders have already been classified, a full description of all rings of a given order remains unknown. The purpose of this paper is to classify all finite rings (up to isomorphism) of a given order. In doing so, we introduce a new concept of quasi basis for certain type of modules, which is a useful computational tool for dealing with finite rings. Then, using this concept, we give structure and isomorphism theorems for finite rings and state our main result to classify (up to isomorphism) the finite rings of a given order. Finally, based on these results, we describe an algorithm to calculate the structure of all such rings. We have implemented our new algorithm in Maple, and we apply it to an example.
An interesting topic in the ring theory is the classification of finite rings. Although rings of certain orders have already been classified, a full description of all rings of a given order remains unknown. The purpose of this paper is to classify all finite rings (up to isomorphism) of a given order. In doing so, we introduce a new concept of quasi basis for certain type of modules, which is a useful computational tool for dealing with finite rings. Then, using this concept, we give structure and isomorphism theorems for finite rings and state our main result to classify (up to isomorphism) the finite rings of a given order. Finally, based on these results, we describe an algorithm to calculate the structure of all such rings. We have implemented our new algorithm in Maple, and we apply it to an example.
DOI : 10.1007/s10587-014-0124-7
Classification : 16P10, 16Z05, 68W30
Keywords: classification of finite ring; finite abelian group; quasi base 
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     title = {Classification of finite rings: theory and algorithm},
     journal = {Czechoslovak Mathematical Journal},
     pages = {641--658},
     year = {2014},
     volume = {64},
     number = {3},
     doi = {10.1007/s10587-014-0124-7},
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     zbl = {06391517},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0124-7/}
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Behboodi, Mahmood; Beyranvand, Reza; Hashemi, Amir; Khabazian, Hossein. Classification of finite rings: theory and algorithm. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 641-658. doi: 10.1007/s10587-014-0124-7

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