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}
}