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Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

CiteScore 2018: 0.44

SCImago Journal Rank (SJR) 2018: 0.325
Source Normalized Impact per Paper (SNIP) 2018: 0.987

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Volume 22, Issue 5-6


On the algebras of almost minimal rank

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


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.

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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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