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

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