Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-07-08T03:43:12.658Z Has data issue: false hasContentIssue false
  • English
  • Français

On Traces of Separable Simple Sub Algebras in Matrix Rings

Published online by Cambridge University Press:  20 November 2018

Takasi Nagahara  and
Seiya Yokota
Takasi Nagahara
Affiliation:
Department of Mathematics, Okayama University, Okayama 700, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For the trace map on an irreducible semigroup of n × n matrices over a field, I. N. Herstein presented a theorem in [3] which enables us to limit the nature of matrix groups of a certain kind. However, this is incorrect in general. For the theorem, we shall present a counter example, a revision, and some generalizations to non-irreducible semigroups.

Keywords

16H0516S50trace mapsseparable algebrasmatrix rings
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 1 , 01 March 1995 , pp. 104 - 111
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Cohn, P. M., Algebra, Vol. 2, Wiley, London, 1977.Google Scholar
2. DeMeyer, F. and Ingraham, E., Separable algebras over commutative rings, Lecture Notes In Math. 181, Springer-Verlag, 1971.Google Scholar
3. Herstein, I. N., Noncommutative rings, Cams Math. Monographs 15, Math. Association of America, Washington, D. C, 1968.Google Scholar
4. Jacobson, N., Basic Algebra II, Freeman, San Francisco, 1980.Google Scholar
5. Jacobson, N., Lectures in abstract algebra II, Linear algebra, New York, 1953.Google Scholar
6. Jacobson, N., Structure of rings, Providence, 1956.Google Scholar
7. Kaplansky, I., Notes on Ring Theory, University of Chicago Math. Lecture Notes, 1965.Google Scholar
8. Tominaga, H. and Nagahara, T., Galois Theory of simple rings, Okayama Math. Lectures, Okayama, 1970.Google Scholar