Burnside's Theorem on Algebras of Matrices

DOI10.2307/2320789zbMath0452.15002OpenAlexW4241410935MaRDI QIDQ3898611

I. Halperin, Peter Rosenthal

Publication date: 1980

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2320789

zbMATH Keywords

algebras of matricesBurnside's theorem

Mathematics Subject Classification ID

Linear transformations, semilinear transformations (15A04) Vector spaces, linear dependence, rank, lineability (15A03)

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The matrix equation \(\log (XY)=\log (X)+\log (Y)\) ⋮ On \(F\)-algebras of algebraic matrices over a subfield \(F\) of the center of a division ring ⋮ On irreducible algebras spanned by triangularizable matrices ⋮ Finite orbits for large groups of automorphisms of projective surfaces ⋮ Finite-dimensional irreducible modules of the universal Askey-Wilson algebra at roots of unity ⋮ Theorems of Burnside and Wedderburn revisited ⋮ On the codimension of subalgebras of the algebra of matrices over a field ⋮ Endomorphism rings of modules and lattices of submodules ⋮ A remark on Burnside's theorem on matrix algebras ⋮ On irreducible and transitive subalgebras in matrix algebras ⋮ Burnside's theorem for matrix rings over division rings ⋮ The simplest proof of Burnside's theorem on matrix algebras ⋮ On the equationAB=BXin collections of matrices

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