Noetherianity and Specht problem for varieties of bicommutative algebras
Rings and Algebras
2018-01-03 v2
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.
Keywords
Cite
@article{arxiv.1706.02529,
title = {Noetherianity and Specht problem for varieties of bicommutative algebras},
author = {Vesselin Drensky and Bekzat K. Zhakhayev},
journal= {arXiv preprint arXiv:1706.02529},
year = {2018}
}
Comments
LATEX, 10 pages, to appear in Journal of Algebra, Available online 28 December 2017