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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
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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