On Shirshov bases of graded algebras. (Q375749)
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scientific article; zbMATH DE number 6221610
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Shirshov bases of graded algebras. |
scientific article; zbMATH DE number 6221610 |
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On Shirshov bases of graded algebras. (English)
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31 October 2013
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Let \(A\) be a finitely generated associative algebra graded by a finite group \(G\). The main result of the note under review is the following generalization of the famous Height Theorem proved by Shirshov. If the neutral component \(A_e\) of \(A\) has a Shirshov basis of height \(h\) then \(A\) admits a Shirshov basis of height \((h+1)|G|\). The proof relies on a purely combinatorial (and very clever) argument.
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Shirshov height theorem
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graded algebras
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Shirshov bases
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