Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T02:11:04.442Z Has data issue: false hasContentIssue false

A Note on Radical Extensions of Rings

Published online by Cambridge University Press:  20 November 2018

M. Chacron
Affiliation:
Carleton University, Ottawa, Ontario, Canada
J. Lawrence
Affiliation:
Carleton University, Ottawa, Ontario, Canada
D. Madison
Affiliation:
Carleton University, Ottawa, Ontario, Canada
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.

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
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