Algorithm to compute abelian subalgebras and ideals in Malcev algebras

Abstract

Communicated by J. Vigo-AguiarIn this paper, we introduce an algorithmic procedure that computes abelian subalgebras and ideals of a given finitedimensional Malcev algebra. All the computations are performed by using the non-zero brackets in the law of the algebra as input. Additionally, the algorithm also computes the˛andˇinvariants of these algebras, and as a supporting output, a list of abelian ideals and subalgebras of maximal dimension is returned too. To implement this algorithm, we have used the symbolic computation package MAPLE 12, performing a brief computational and statistical study for it and its implementation.

On finite division rings with a designed automorphism group

“…Computational tools have been naturally considered in the study of associative and nonassociative algebras (even over finite fields) . During the last few years, computational efforts in order to classify some of these objects have been made.…”

“…Computational tools have been naturally considered in the study of associative and nonassociative algebras (even over finite fields). 8,9 During the last few years, computational efforts in order to classify some of these objects have been made. For instance, the classification of finite division rings, also called semifields, with 64 elements, is completely known, 10 as well as those with 243 elements.…”