Inner derivations of division rings and canonical Jordan form of triangular operators

Author:
Dragomir Ž. Đoković

Journal:
Proc. Amer. Math. Soc. **94** (1985), 383-386

MSC:
Primary 16A39; Secondary 15A33

DOI:
https://doi.org/10.1090/S0002-9939-1985-0787877-7

MathSciNet review:
787877

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a division ring and its center. We show that a generalized canonical Jordan form exists for triangularizable matrices over which are algebraic over , i.e, satisfy for some nonzero polynomial over . This canonical form is a direct sum of generalized Jordan blocks . This block is an by matrix whose diagonal entries are equal to , those on the first superdiagonal are equal to , and all other entries are equal to zero. If is separable over then we can choose , but in general this cannot be done.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0787877-7

Keywords:
Annihilator,
Jordan-Hölder series,
generalized Jordan blocks,
irreducible polynomial,
bounded module,
similarity

Article copyright:
© Copyright 1985
American Mathematical Society