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1 results

  • Comparing Graded Versions of the Prime Radical

  • M. A. Beattie, Liu S.X., P. N. Stewart
  • Journal:
    Canadian Mathematical Bulletin / Volume 34 / Issue 2 / 01 June 1991
    Published online by Cambridge University Press:
    20 November 2018, pp. 158-164
    Print publication:
    01 June 1991
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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).