Gelfand-Kirillov dimension of bicommutative algebras. Issue 22 (21st December 2022) - Bai, Yuxiu; Chen, Yuqun; Zhang, Zerui
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 Gröbner–Shirshov bases theory for bicommutative algebras, and show that every finitely generated bicommutative algebra has a finite Gröbner–Shirshov basis. As an application, we show that the Gelfand-Kirillov dimension of a finitely generated bicommutative algebra is a nonnegative integer.