Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-23T19:34:31.110Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on the Density Theorem

Published online by Cambridge University Press:  20 November 2018

John Lawrence
John Lawrence*
Affiliation:
The University of Chicago and the University of Waterloo
Rights & Permissions [Opens in a new window]

Extract

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.

In this note we prove:

Theorem. Let R be a right primitive ring with pair-wise non-isomorphic faithful irreducible modules Ml, M2,…, Mk. Let Di = EndR Mi. For each i, let be elements of Mi linearly independent over Di. For each i, let be a set of elements of Mi. Then there exists an element r of R such that uij = vijr, for i = 1, 2, …, k and j = 1, 2, …, ni.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 2 , 01 June 1981 , pp. 249
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Herstein, , Noncommutative rings, Carus Monograph, Math. Assoc, of America, (1968).Google Scholar