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2019 An improved bound for the lengths of matrix algebras
Yaroslav Shitov
Algebra Number Theory 13(6): 1501-1507 (2019). DOI: 10.2140/ant.2019.13.1501

Abstract

Let S be a set of n × n matrices over a field F . We show that the F -linear span of the words in S of length at most

2 n log 2 n + 4 n

is the full F -algebra generated by S . This improves on the n 2 3 + 2 3 bound by Paz (1984) and an O ( n 3 2 ) bound of Pappacena (1997).

Citation

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Yaroslav Shitov. "An improved bound for the lengths of matrix algebras." Algebra Number Theory 13 (6) 1501 - 1507, 2019. https://doi.org/10.2140/ant.2019.13.1501

Information

Received: 14 November 2018; Revised: 6 March 2019; Accepted: 14 May 2019; Published: 2019
First available in Project Euclid: 21 August 2019

zbMATH: 07103983
MathSciNet: MR3994574
Digital Object Identifier: 10.2140/ant.2019.13.1501

Subjects:
Primary: 15A03
Secondary: 15A30

Keywords: finite-dimensional algebras , generating sets , matrix theory

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 6 • 2019
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