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arXiv · 2107.00454

Gelfand-Kirillov dimension of bicommutative algebras

Yuxiu Bai·Yuqun Chen·Zerui Zhang
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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.

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Yuxiu Bai, Yuqun Chen, Zerui Zhang. 2021-07-01. Gelfand-Kirillov dimension of bicommutative algebras. https://arxiv.org/abs/2107.00454

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