Gröbner–Shirshov Bases Theory for Trialgebras

Juwei Huang and Yuqun Chen
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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

Mathematics, 2021, vol. 9, issue 11, 1-23

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.

Keywords: Gröbner–Shirshov basis; normal form; Gelfand–Kirillov dimension; trialgebra; trisemigroup (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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