EAKIN-NAGATA THEOREM FOR COMMUTATIVE RINGS WHOSE REGULAR IDEALS ARE FINITELY GENERATED

  • Received : 2010.08.04
  • Accepted : 2010.08.20
  • Published : 2010.09.30

Abstract

Let R be a commutative ring with identity, T(R) be the total quotient ring of R, and D be a ring such that $R{\subseteq}D{\subseteq}T(R)$ and D is a finite R-module. In this paper, we show that each regular ideal of R is finitely generated if and only if each regular ideal of D is finitely generated. This is a generalization of the Eakin-Nagata theorem that R is Noetherian if and only if D is Noetherian.

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