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SOME REMARKS ON TYPES OF NOETHERIAN LOCAL RINGS

  • Lee, Kisuk (Department of Mathematics Sookmyung Women's University)
  • Received : 2014.08.13
  • Accepted : 2014.10.10
  • Published : 2014.11.15

Abstract

We study some results which concern the types of Noetherian local rings, and improve slightly the previous result: For a complete unmixed (or quasi-unmixed) Noetherian local ring A, we prove that if either $A_p$ is Cohen-Macaulay, or $r(Ap){\leq}depth$ $A_p+1$ for every prime ideal p in A, then A is Cohen-Macaulay. Also, some analogous results for modules are considered.

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