English

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