Gelfand-Kirillov dimension of bicommutative algebras. Issue 22 (21st December 2022)

• Record Type: Journal Article
• Authors: Bai, Yuxiu; Chen, Yuqun; Zhang, Zerui
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 22(2022)
• Page Start: 7623
• Page End: 7649
• Publication Date: 2022-12-21
• Subjects: Commutative algebra -- bicommutative algebra -- Gelfand-Kirillov dimension -- Gröbner basis -- Gröbner–Shirshov basis; 13P10 -- 16S15 -- 16P90 -- 17A30 -- 17A61; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1999890
• Languages: English
• ISSNs: 0308-1087

Abstract

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.