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New Operated Polynomial Identities and Gröbner-Shirshov Bases

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jinwei Wang & Zhicheng Zhu & Xing Gao, 2022. "New Operated Polynomial Identities and Gröbner-Shirshov Bases," Mathematics, MDPI, vol. 10(6), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:961-:d:773264
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