Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON TYPES OF NOETHERIAN LOCAL RINGS AND MODULES

  • Lee, Ki-Suk (DEPARTMENT OF MATHEMATICS SOOKMYUNG WOMEN'S UNIVERSITY)
  • Published : 2007.07.30
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Abstract

We investigate some results which concern the types of Noetherian local rings. In particular, we show that if r(Ap) ${\le}$ depth Ap + 1 for each prime ideal p of a quasi-unmixed Noetherian local ring A, then A is Cohen-Macaulay. It is also shown that the Kawasaki conjecture holds when dim A ${\le}$ depth A + 1. At the end, we deal with some analogous results for modules, which are derived from the results studied on rings.

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References

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Cited by

  1. SOME REMARKS ON TYPES OF NOETHERIAN LOCAL RINGS vol.27, pp.4, 2014, https://doi.org/10.14403/jcms.2014.27.4.625