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Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

6 Issues per year


CiteScore 2016: 0.16

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.552

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1569-3929
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Volume 22, Issue 5-6

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On the algebras of almost minimal rank

V. V. Lysikov
Published Online: 2013-06-22 | DOI: https://doi.org/10.1515/dma-2012-034

Abstract

We consider the bilinear complexity of multiplication in local and semisimple algebras over an infinite field of characteristic differing from 2. We obtain a criterion for the rank of a local algebra to be almost minimal. We evaluate the bilinear complexity of the algebras of generalised quaternions over such a field; we prove that any simple algebra of almost minimal rank is an algebra of generalised quaternions. This result is used for the classification of semisimple algebras of almost minimal rank.

About the article

Published Online: 2013-06-22

Published in Print: 2012-10-01


Citation Information: Discrete Mathematics and Applications, Volume 22, Issue 5-6, Pages 493–510, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265, DOI: https://doi.org/10.1515/dma-2012-034.

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