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A Note on Radical Extensions of Rings
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1975
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