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Semigroup Graded Rings and Jacobson Rings

In: Lattices, Semigroups, and Universal Algebra

Author

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  • Eric Jespers

    (Memorial University of Newfoundland, Dept. Mathematics and Statistics)

Abstract

We study when some graded rings are Jacobson rings. In particular we obtain that rings strongly graded either by a polycyclic-by-finite group, or by an abelian group of finite torsion free rank are Jacobson rings in case the identity component is a left Noetherian Jacobson ring. For monoid rings R[S] of abelian monoids of finite rank the same result holds without R being left Noetherian.

Suggested Citation

  • Eric Jespers, 1990. "Semigroup Graded Rings and Jacobson Rings," Springer Books, in: Jorge Almeida & Gabriela Bordalo & Philip Dwinger (ed.), Lattices, Semigroups, and Universal Algebra, pages 105-114, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-2608-1_12
    DOI: 10.1007/978-1-4899-2608-1_12
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