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arXiv · 1706.02529

Noetherianity and Specht problem for varieties of bicommutative algebras

Vesselin Drensky·Bekzat K. Zhakhayev
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Abstract

Nonassociative algebras satisfying the polynomial identities x(yz)=y(xz) and (xy)z=(xz)y are called bicommutative. We prove the following results: (i) Finitely generated bicommutative algebras are weakly noetherian, i.e., satisfy the ascending chain condition for two-sided ideals. (ii) We give the positive solution to the Specht problem (or the finite basis problem) for varieties of bicommutative algebras over an arbitrary field of any characteristic.

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Vesselin Drensky, Bekzat K. Zhakhayev. 2017-06-08. Noetherianity and Specht problem for varieties of bicommutative algebras. https://doi.org/10.1016/j.jalgebra.2017.12.012

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