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.
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Bai et al. (2021) studied this question.
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