대한수학회지 (Journal of the Korean Mathematical Society)

  • 제39권4호
  • /
  • Pages.611-620
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  • 2002
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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STRUCTURE OF THE FLAT COVERS OF ARTINIAN MODULES

  • Payrovi, S.H. (Imam Khomeini International University)
  • 발행 : 2002.07.01
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초록

The aim of the Paper is to Obtain information about the flat covers and minimal flat resolutions of Artinian modules over a Noetherian ring. Let R be a commutative Noetherian ring and let A be an Artinian R-module. We prove that the flat cover of a is of the form $\prod_{p\epsilonAtt_R(A)}T-p$, where $Tp$ is the completion of a free R$_{p}$-module. Also, we construct a minimal flat resolution for R/xR-module 0: $_AX$ from a given minimal flat resolution of A, when n is a non-unit and non-zero divisor of R such that A = $\chiA$. This result leads to a description of the structure of a minimal flat resolution for ${H^n}_{\underline{m}}(R)$, nth local cohomology module of R with respect to the ideal $\underline{m}$, over a local Cohen-Macaulay ring (R, $\underline{m}$) of dimension n.

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참고문헌

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피인용 문헌

  1. Minimal Flat Resolutions of Artinian Modules vol.12, pp.03, 2005, https://doi.org/10.1142/S1005386705000404