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On types of Noetherian local rings and modules

Authors
Lee, Kisuk
Issue Date
Jul-2007
Publisher
KOREAN MATHEMATICAL SOCIETY
Keywords
Cohen-Macaulay ring; type of a ring; Gorenstein ring
Citation
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, v.44, no.4, pp.987 - 995
Journal Title
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
Volume
44
Number
4
Start Page
987
End Page
995
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/14668
DOI
10.4134/JKMS.2007.44.4.987
ISSN
0304-9914
Abstract
We investigate some results which concern the types of Noetherian local rings. In particular, we show that if r (Ap) <= 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 <= 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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