A spatial version of Wedderburn’s Principal Theorem

DOI10.1080/03081087.2014.925452zbMath1373.15028OpenAlexW2049921035MaRDI QIDQ5175391

Heydar Radjavi, Leo Livshits, Laurent W. Marcoux, Gordon Wilson MacDonald

Publication date: 20 February 2015

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10012/15737

zbMATH Keywords

invariant subspacesWedderburn-Artin theoremtriangular similarityirreducible matrix algebrasWedderburn's principal theoremalgebra of all linear transformationsblock upper triangular matrix algebrassemi-simple matrix algebras

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Finite rings and finite-dimensional associative algebras (16P10) Prime and semiprime associative rings (16N60) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Algebraic systems of matrices (15A30) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Finite-dimensional division rings (16K20) Canonical forms, reductions, classification (15A21)

Related Items (3)

Matrix algebras with a certain compression property. II ⋮ Matrix algebras with a certain compression property. I ⋮ Common invariant subspaces from small commutators

Cites Work

• Block triangularization of algebras of matrices
• Paratransitive algebras of linear operators. I
• Paratransitive algebras of linear operators. II
• Simple Lie algebras over a field of characteristic zero

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