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3 results

  • On Extending Projectives of Finite Group-Graded Algebras

  • Morton E. Harris
  • Journal:
    Canadian Mathematical Bulletin / Volume 34 / Issue 2 / 01 June 1991
    Published online by Cambridge University Press:
    20 November 2018, pp. 224-228
    Print publication:
    01 June 1991
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  • Let G be a finite group, let k be a field and let R be a finite dimensional fully G-graded k-algebra. Also let L be a completely reducible R-module and let P be a projective cover of R. We give necessary and sufficient conditions for P|R1 to be a projective cover of L|R1 in Mod (R1). In particular, this happens if and only if L is R1-projective. Some consequences in finite group representation theory are deduced.

  • 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).

  • On invariant radicals

  • A. D. Sands
  • Journal:
    Canadian Mathematical Bulletin / Volume 32 / Issue 2 / 01 June 1989
    Published online by Cambridge University Press:
    20 November 2018, pp. 255-256
    Print publication:
    01 June 1989
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  • It is shown that the concepts of normal radical as introduced by Jaegermann [2] and of invariant radical as introduced by Anderson, Divinsky and Sulinski [1] are equivalent.