New Operated Polynomial Identities and Gröbner-Shirshov Bases

Jinwei Wang, Zhicheng Zhu and Xing Gao
Additional contact information
Jinwei Wang: School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China
Zhicheng Zhu: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
Xing Gao: School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, China

Mathematics, 2022, vol. 10, issue 6, 1-15

Abstract: Twenty years ago, Rota posed the problem of finding all possible algebraic identities that can be satisfied by a linear operator on an algebra, named Rota’s Classification Problem later. Rota’s Classification Problem has proceeded two steps to understand it and has been studied actively recently. In particular, the method of Gröbner-Shirshov bases has been used successfully in the study of Rota’s Classification Problem. Quite recently, a new approach introduced to Rota’s Classification Problem and classified some (new) operated polynomial identities. In this paper, we prove that all operated polynomial identities classified via this new approach are Gröbner-Shirshov. This gives a partial answer of Rota’s Classification Problem.

Keywords: Rota’s classification problem; operated associative algebras; rewriting systems; Gröbner-Shirshov basis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/6/961/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/6/961/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:6:p:961-:d:773264

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().