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Keywords = trisemigroup

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23 pages, 338 KB  
Article
Gröbner–Shirshov Bases Theory for Trialgebras
by Juwei Huang and Yuqun Chen
Mathematics 2021, 9(11), 1207; https://doi.org/10.3390/math9111207 - 26 May 2021
Cited by 5 | Viewed by 3203
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 [...] Read more.
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. Full article
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