2022•Journal of Algebra and Its ApplicationsRequires access

Defining identities for mono and binary Zinbiel algebras

Nurlan Ismailov, Farukh Mashurov, Nurken Smadyarov

Abstract

An algebra is said to be a mono Zinbiel algebra if each of its one-generated subalgebra is a Zinbiel algebra. An algebra is said to be a binary Zinbiel algebra if each of its two-generated subalgebra is a Zinbiel algebra. We give an independent set of defining identities for mono and binary Zinbiel algebras.

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Key concepts: Subalgebra, Mathematics, Cellular algebra, Binary operation, Algebra over a field, Division algebra, Filtered algebra, Algebra representation