English

Gelfand-Kirillov dimension of bicommutative algebras

Rings and Algebras 2021-07-02 v1

Abstract

We first offer a fast method for calculating the Gelfand-Kirillov dimension of a finitely presented commutative algebra by investigating certain finite set. Then we establish a Groebner-Shirshov bases theory for bicommutative algebras, and show that every finitely generated bicommutative algebra has a finite Groebner-Shirshov basis. As an application, we show that the Gelfand-Kirillov dimension of a finitely generated bicommutative algebra is a nonnegative integer.

Keywords

Cite

@article{arxiv.2107.00454,
  title  = {Gelfand-Kirillov dimension of bicommutative algebras},
  author = {Yuxiu Bai and Yuqun Chen and Zerui Zhang},
  journal= {arXiv preprint arXiv:2107.00454},
  year   = {2021}
}