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The nucleus of the free alternative algebra. (English) Zbl 1147.17006

The authors use a computer procedure to determine a basis of the elements of degree 5 in the nucleus of the free alternative algebra. In order to save computer memory, they do their calculations over the field \(\mathbb Z_{103}\). All calculations are made with multilinear identities. Their procedure is also valid for other characteristics and for determining nuclear elements of higher degree.

MSC:

17D05 Alternative rings
17-04 Software, source code, etc. for problems pertaining to nonassociative rings and algebras
17-08 Computational methods for problems pertaining to nonassociative rings and algebras