The homogeneous spectrum of a graded commutative ring

William Heinzer, Moshe Roitman

Research output: Contribution to journalArticlepeer-review


Suppose Γ is a torsion-free cancellative commutative monoid for which the group of quotients is finitely generated. We prove that the spectrum of a Γ-graded commutative ring is Noetherian if its homogeneous spectrum is Noetherian, thus answering a question of David Rush. Suppose A is a commutative ring having Noetherian spectrum. We determine conditions in order that the monoid ring A[Γ] have Noetherian spectrum. If rank Γ ≤ 2, we show that A[Γ] has Noetherian spectrum, while for each n ≥ 3 we establish existence of an example where the homogeneous spectrum of A[Γ] is not Noetherian.

Original languageEnglish
Pages (from-to)1573-1580
Number of pages8
JournalProceedings of the American Mathematical Society
Issue number6
StatePublished - 2002
Externally publishedYes


  • Graded ring
  • Homogeneous spectrum
  • Noetherian spectrum
  • Torsion-free cancellative commutative monoid

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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