On α-like radicals

Authors

  • Halina France-Jackson

Keywords:

prime like radical, α-like radical, special radical, Amitsur property of radicals, polynomially extensible radicals

Abstract

A radical Ï is called prime-like if for every prime ring A, the polynomial ring A[x] is Ï-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-likness is a generalization of prime-likness and extend some results concerning prime like radicals. This allows us to easily find distinct special radicals which coincide on simple rings and on polynomial rings which answers a question put by M. Ferrero.

Published

2011-10-19

Issue

Vol. 84 No. 1 (2011)

Section

Articles
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