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Gröbner-Shirshov Bases Theory for Trialgebras
Version 1
: Received: 17 April 2021 / Approved: 19 April 2021 / Online: 19 April 2021 (15:19:28 CEST)
A peer-reviewed article of this Preprint also exists.
Huang, J.; Chen, Y. Gröbner–Shirshov Bases Theory for Trialgebras. Mathematics 2021, 9, 1207. Huang, J.; Chen, Y. Gröbner–Shirshov Bases Theory for Trialgebras. Mathematics 2021, 9, 1207.
Abstract
We establish a Gröbner-Shirshov bases theory for trialgebras and show that every ideal of a free trialgebra has a unique reduced Gröbner-Shirshov basis. 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
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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