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.
Acknowledgments
The authors would like to thank the referee for his/her insightful comments and valuable suggestions. The authors are also grateful to L. A. Bokut and Yu Li for bringing the topic of bicommutative algebras to our attention.
Disclosure statement
No potential conflict of interest was reported by the author(s).