Burnside's theorem for matrix rings over division rings

DOI10.1016/j.laa.2003.08.011zbMath1068.15019OpenAlexW2069459603MaRDI QIDQ1826831

Bamdad R. Yahaghi, Peter Rosenthal, Mehdi Radjabalipour

Publication date: 6 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.laa.2003.08.011

zbMATH Keywords

quaternionscounterexamplesBurnside's theoremDivision ringInvariant (right) subspaceIrreducible (left) algebraMatrix (left) algebraSubmodule

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Algebraic systems of matrices (15A30) Linear transformations, semilinear transformations (15A04)

Related Items

On \(F\)-algebras of algebraic matrices over a subfield \(F\) of the center of a division ring ⋮ Multiplicity and indiscernibility ⋮ On irreducible algebras spanned by triangularizable matrices ⋮ On real algebras generated by positive and nonnegative matrices ⋮ Theorems of Burnside and Wedderburn revisited ⋮ Algebraic prime subalgebras in simple Artinian algebras. ⋮ Systems of generators of matrix incidence algebras over finite fields ⋮ On irreducible and transitive subalgebras in matrix algebras ⋮ On irreducible semigroups of matrices with traces in a subfield

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• Unipotent Matrix Groups Over Division Rings
• Quaternions and matrices of quaternions