Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

STRUCTURE OF THE FLAT COVERS OF ARTINIAN MODULES

  • Payrovi, S.H. (Imam Khomeini International University)
  • Published : 2002.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  1. Bull. London Math. Soc. v.33 no.4 All modules have flat covers L. Bican;R. El Bashir;E. Enochs https://doi.org/10.1017/S0024609301008104
  2. Local cohomology: an algebraic introduction with geometric applications M. P. Brodmann;R. Y. Sharp
  3. Israel J. Math. v.39 Injective and flat covers, envelopes and resolvents E. Enochs https://doi.org/10.1007/BF02760849
  4. Proc. Amer. Math. Soc. v.92 Flat covers and flat cotorsion modules E. Enochs https://doi.org/10.2307/2045180
  5. J. Algebra v.105 Minimal pure injective resolutions of flat modules E. Enochs https://doi.org/10.1016/0021-8693(87)90200-6
  6. Comment. Math. Univ. Carolin v.35 On Cohen-Macaulay rings E. Enochs;O. Jenda
  7. Proc. Amer. Math. Soc. v.125 On invariants dual to the Bass numbers E. Enochs;J. Xu https://doi.org/10.1090/S0002-9939-97-03662-9
  8. Symposia Mathematica v.11 Secondary representation of modules over a cimmutative ring I. G. MacDonald
  9. Pacific J. Math. v.8 Injective modules over Noetherian rings E, Matlis https://doi.org/10.2140/pjm.1958.8.511
  10. Proc. Edinburgh Math. Soc. v.38 The Co-localization of an Artinian module L. Melkersson;P. Schenzel https://doi.org/10.1017/S0013091500006258
  11. J. Algebra v.175 Mininal injective and flat resolutions of modules over gorenstein rings J. Xu https://doi.org/10.1006/jabr.1995.1196
  12. Lecture Notes in Mathematics v.1634 Flat covers of modules J. Xu

Cited by

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