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Four-dimensional nilpotent diassociative algebras. (English) Zbl 1394.16053

Summary: The paper is devoted to structural properties of diassociative algebras. We introduce the notions of nilpotency, solvability of the diassociative algebras and study their properties. The list of all possible nilpotent diassociative algebra structures on four-dimensional complex vector spaces is given.

MSC:

16W99 Associative rings and algebras with additional structure
17A30 Nonassociative algebras satisfying other identities
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Full Text: Euclid