Gelfand-Kirillov dimension of bicommutative algebras
Yuxiu Bai, Yuqun Chen, Zerui Zhang
TL;DR
This paper introduces a fast method to compute the Gelfand-Kirillov dimension of finitely presented commutative algebras, develops a Groebner-Shirshov bases theory for bicommutative algebras, and proves the dimension is always a nonnegative integer.
Contribution
It provides a new computational approach for Gelfand-Kirillov dimension and establishes foundational basis theory for bicommutative algebras.
Findings
Gelfand-Kirillov dimension is a nonnegative integer for finitely generated bicommutative algebras.
A finite Groebner-Shirshov basis exists for all finitely generated bicommutative algebras.
A fast method for calculating Gelfand-Kirillov dimension is proposed.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology