On vanishing of certain Ext modules
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概要
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Let R be a Noetherian local ring with the maximal ideal \mathfrak{m} and dim R = 1. In this paper, we shall prove that the module Ext1R (R/Q, R) does not vanish for every parameter ideal Q in R, if the embedding dimension \mathrm{v}(R) of R is at most 4 and the ideal \mathfrak{m}2 kills the 0^{\underline{th}} local cohomology module H\mathfrak{m}0(R). The assertion is no longer true unless v(R) ≤ 4. Counterexamples are given. We shall also discuss the relation between our counterexamples and a problem on modules of finite G-dimension.
- 2008-10-01
著者
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GOTO Shiro
Department of Mathematics School of Science and Technology Meiji University
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HAYASAKA Futoshi
Department of Mathematics School of Science and Technology Meiji University
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TAKAHASHI Ryo
Department of Mathematical Sciences Faculty of Science Shinshu University
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Goto Shiro
Department Of Mathematic School Of Science And Technology Meiji University
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Takahashi Ryo
Department of Electrical Engineering, Kyoto University
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