Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 787877
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ D$ be a division ring and $ k$ its center. We show that a generalized canonical Jordan form exists for triangularizable matrices $ A$ over $ D$ which are algebraic over $ k$, i.e, satisfy $ f(A) = 0$ for some nonzero polynomial $ f$ over $ k$. This canonical form is a direct sum of generalized Jordan blocks $ {J_m}(\alpha ,\beta )$. This block is an $ m$ by $ m$ matrix whose diagonal entries are equal to $ \alpha $, those on the first superdiagonal are equal to $ \beta $, and all other entries are equal to zero. If $ \alpha $ is separable over $ k$ then we can choose $ \beta = 1$, but in general this cannot be done.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A39, 15A33

Retrieve articles in all journals with MSC: 16A39, 15A33

Additional Information

Keywords: Annihilator, Jordan-Hölder series, generalized Jordan blocks, irreducible polynomial, bounded module, similarity
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society