Computation of isotopisms of algebras over finite fields by means of graph invariants

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• 作者：O.J. Falc&oacute ; n^a ; ^{oscfalgan@yahoo.es} ; R.M. Falc&oacute ; n^b ; ^{rafalgan@us.es} ; J. Nú ; ñ ; ez^a ; ^{jnvaldes@us.es} ; A.M. Pacheco^c ; ^{ampacheco@uloyola.es} ; M.T. Villar^a ; ^villar@us.es
• 关键词：05C25 ; 05C30 ; 05B15
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：July 2017
• 年：2017
• 卷：318
• 期：Complete
• 页码：307-315
• 全文大小：453 K
• 卷排序：318

文摘

In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually required to determine whether two algebras are isomorphic. In order to illustrate their efficiency, we determine explicitly the classification of two- and three-dimensional partial quasigroup rings.