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Gröbner–Shirshov Bases Theory for Trialgebras

Author

Listed:
  • Juwei Huang

    (School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China)

  • Yuqun Chen

    (School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China)

Abstract

We establish a method of Gröbner–Shirshov bases for trialgebras and show that there is a unique reduced Gröbner–Shirshov basis for every ideal of a free trialgebra. As applications, we give a method for the construction of normal forms of elements of an arbitrary trisemigroup, in particular, A.V. Zhuchok’s (2019) normal forms of the free commutative trisemigroups are rediscovered and some normal forms of the free abelian trisemigroups are first constructed. Moreover, the Gelfand–Kirillov dimension of finitely generated free commutative trialgebra and free abelian trialgebra are calculated, respectively.

Suggested Citation

  • Juwei Huang & Yuqun Chen, 2021. "Gröbner–Shirshov Bases Theory for Trialgebras," Mathematics, MDPI, vol. 9(11), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1207-:d:562855
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    Cited by:

    1. Sergey Victor Ludkowski, 2023. "Nonassociative Algebras, Rings and Modules over Them," Mathematics, MDPI, vol. 11(7), pages 1-33, April.

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