Author:
Chacron M.,Lawrence J.,Madison D.
Abstract
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.
Publisher
Canadian Mathematical Society
Cited by
4 articles.
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1. HYPERCOMMUTING VALUES IN ASSOCIATIVE RINGS WITH UNITY;Journal of the Australian Mathematical Society;2013-03-08
2. RINGS SATISFYING GENERALIZED ENGEL CONDITIONS;Journal of Algebra and Its Applications;2012-11-14
3. Root Extensions and Factorization in Affine Domains;Canadian Mathematical Bulletin;2010-06-01
4. On a conjecture by Herstein;Journal of Algebra;1989-10