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A Note on Types of Noetherian Local Rings
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Abstract
In this note we investigate some results which concern the typesof local rings. In particular it is shown that if the type of aquasi-unmixed local ring A is less than or equal tomathrm{depth} ,A + 1, and hat{A}_{p} is Cohen-Macaulay forevery prime p not= hat{m}, then A is Cohen-Macaulay. (Thisimplies the previously known result: if hat{A} satisfies(S_{n-1}), where n is the type of a ring A, then A isCohen-Macaulay.)
관련 논문AI추천
On types of Noetherian local rings and modules이기석대한수학회 · 대한수학회지2007 · 제44권 제4호Note on Good Ideals in Gorenstein Local Rings김미경대한수학회 · 대한수학회보2002 · 제39권 제3호A Note on -Separative ModulesHuanyin Chen경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2007 · 제47권 제3호Simple valuation ideals of order two in$2$-dimensional regular local rings노선숙, 이혜숙, 홍주연대한수학회 · 대한수학회논문집2005 · 제20권 제3호On column invariant and index of Cohen-Macaulay local rings이기석, Jee Koh대한수학회 · 대한수학회지2006 · 제43권 제4호$\Pi$-coherent dimensions and $\Pi$-coherent ringsLixin Mao대한수학회 · 대한수학회지2007 · 제44권 제3호
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