Commutative matrix subalgebras and length function

It is proved that if the length of a commutative matrix subalgebra is maximal then this subalgebra is maximal under inclusion. The examples are given showing that the converse does not hold. To establish this result, we prove several fundamental properties of the length function.

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Bibliographic Details
Published inLinear algebra and its applications Vol. 430; no. 7; pp. 1790 - 1805
Main Authors Guterman, A.E., Markova, O.V.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.04.2009
Subjects
Commutative matrix algebras
Finite-dimensional algebras
Matrix length
Commutative matrix algebras
Finite-dimensional algebras
Secondary: 15A18
Matrix length
Primary: 13E10, 15A27
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Summary:It is proved that if the length of a commutative matrix subalgebra is maximal then this subalgebra is maximal under inclusion. The examples are given showing that the converse does not hold. To establish this result, we prove several fundamental properties of the length function.
ISSN:0024-3795
DOI:10.1016/j.laa.2008.07.010