Free Products of Trialgebras
Juwei Huang, Yuqun Chen, Zerui Zhang
TL;DR
This paper introduces a general method for constructing free products of trialgebras and trioids using Gr"obner-Shirshov bases, solving an open problem in the field.
Contribution
It applies Gr"obner-Shirshov bases to develop a unified approach for free products of trialgebras and trioids, addressing previously unresolved questions.
Findings
Successfully constructs free products of trialgebras and trioids
Provides a solution to Zhuchok's open problem
Establishes a general framework for replicated algebras
Abstract
We apply the method of Gr\"obner-Shirshov bases for replicated algebras developed by Kolesnikov to offer a general approach for constructing free products of trialgebrs (resp. trioids). In particular, the open problem of Zhuchok on constructing free products of trioids is solved.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology