On Shirshov bases of graded algebras
Fedor Petrov, Pasha Zusmanovich
TL;DR
This paper proves that if the neutral component of a finitely-generated graded algebra has a Shirshov base, then the entire algebra also possesses a Shirshov base, extending properties from a component to the whole algebra.
Contribution
It establishes a new result linking the Shirshov base property of the neutral component to the entire finitely-generated graded algebra.
Findings
Neutral component having a Shirshov base implies the whole algebra does
The result applies to finitely-generated associative algebras graded by finite groups
Extends understanding of Shirshov bases in graded algebra structures
Abstract
We prove that if the neutral component in a finitely-generated associative algebra graded by a finite group has a Shirshov base, then so does the whole algebra.
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