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Classification of finite rings: theory and algorithm

Mahmood BehboodiReza BeyranvandAmir HashemiHossein Khabazian — 2014

Czechoslovak Mathematical Journal

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...

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