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Jacobson rings and rings strongly graded by an abelian group

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Abstract

LetR be ring strongly graded by an abelian groupG of finite torsion-free rank. Lete be the identity ofG, andR e the component of degreee ofR. AssumeR e is a Jacobson ring. We prove that graded subrings ofR are again Jacobson rings if eitherR e is a left Noetherian ring orR is a group ring. In particular we generalise Goldie and Michlers’s result on Jacobson polycyclic group rings, and Gilmer’s result on Jacobson commutative semigroup rings of finite torsion-free rank.

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Authors and Affiliations

  1. Department of Mathematics, Memorial University of Newfoundland, A1C 5S7, St. John’s, Newfoundland, Canada

    Eric Jespers

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  1. Eric Jespers
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Jespers, E. Jacobson rings and rings strongly graded by an abelian group. Israel J. Math. 63, 67–78 (1988). https://doi.org/10.1007/BF02765021

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  • DOI: https://doi.org/10.1007/BF02765021

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