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A Note on Radical Extensions of Rings

Published online by Cambridge University Press:  20 November 2018

M. Chacron ,
J. Lawrence  and
D. Madison
M. Chacron
Affiliation:
Carleton University, Ottawa, Ontario, Canada
J. Lawrence
Affiliation:
Carleton University, Ottawa, Ontario, Canada
D. Madison
Affiliation:
Carleton University, Ottawa, Ontario, Canada
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All rings are associative. A ring T is said to be radical over a subring R if for every t ∈ T, there exists a natural number n(t) such that tn(t) ∈ R.

In [1] Faith showed that if T is radical over R and T is primitive, then R is primitive. We might then ask if the same is true if prime is substituted for primitive.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 3 , August 1975 , pp. 423 - 424
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Faith, C., Radical extensions of rings, R.A.M.S. 12 (1961), 274-283.Google Scholar
2. Kaplansky, I., A theorem on division rings, Can. Jour. Math. 3 (1951), 290-293.Google Scholar