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ON α-LIKE RADICALS
Published online by Cambridge University Press: 16 June 2011
Abstract
A radical ρ is called prime-like if for every prime ring A, the polynomial ring A[x] is ρ-semisimple. Let α be a radical satisfying the polynomial equation α(A[x])=(α(A))[x] for every ring A. A radical γ is called α-like if for every α-semisimple ring A, the polynomial ring A[x] is γ-semisimple. In this paper, we study properties of α-like radicals. We show that α-likeness is a generalization of prime-likeness and extend some results concerning prime-like radicals. This allows us easily to find distinct special radicals which coincide on simple rings and on polynomial rings, which answers a question put by Ferrero.
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- Research Article
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- Copyright © Australian Mathematical Publishing Association Inc. 2011
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