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Comparing Graded Versions of the Prime Radical

Published online by Cambridge University Press:  20 November 2018

M. A. Beattie ,
Liu S.X.  and
P. N. Stewart
M. A. Beattie
Affiliation:
Department of Mathematics and Computer Science Mount Allison University Sackville, New Brunswick, Canada E0A 3C0
Liu S.X.
Affiliation:
Department of Mathematics Beijing Normal University Beijing, China
P. N. Stewart
Affiliation:
Department of Mathematics, Statistics and Computing Science Dalhousie University Halifax, Nova Scotia, Canada B3H 3J5
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Abstract

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Let G be a group with identity e, let λ be a normal supernilpotent radical in the category of associative rings and let λref be the reflected radical in the category of G-graded rings. Then for A a G-graded ring, λref(A) is the largest graded ideal of A whose intersection with Ae is λ (Ae). For λ = B, the prime radical, we compare Bref(A) to BG(A) = B(A)G, the largest graded ideal in B(A).

Keywords

16A0316A2116A12.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 2 , 01 June 1991 , pp. 158 - 164
Copyright
Copyright © Canadian Mathematical Society 1991

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