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Paper IPM / M / 7896  


Abstract:  
Let D be a division ring and F a subfield of its center. We
prove a WedderburnArtin type theorem for irreducible Falgebras
of Falgebraic matrices in M_{n}(D). We then use our result to
show that, up to a similarity, M_{n}(F) is the only irreducible
Falgebra of triangularizable matrices in M_{n}(D) with inner
eigenvalues in F provided that such an Falgebra exists. We
use this result to prove a block triangularization theorem, which
is a wellknown result for algebras of matrices over algebraically
closed fields, for Falgebras of triangularizable matrices in
M_{n}(D) with inner eigenvalues in the subfield F of the center
of D. We use our main results to prove the counterparts of some
classical and new triangularization results over a general
division ring. Also, we generalize a wellknown theorem of W.
Burnside to irreducible Falgebras of matrices in M_{n}(K) with
traces in the subfield F of the field K.
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