호남수학학술지 (Honam Mathematical Journal)

  • 제40권2호
  • /
  • Pages.355-366
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  • 2018
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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MINIMAL PROJECTIVE RESOLUTIONS OF A FINITELY GENERATED MODULE M OVER A NOETHERIAN LOCAL RING (R, 𝔪) AND THE COHOMOLOGIES OF (M, R/𝔪)

  • Lee, Sang Cheol (Department of Mathematics Education, and Institute of Pure and Applied Mathematics Chonbuk National University) ;
  • Song, Yeong Moo (Department of Mathematics Education, Sunchon National University)
  • 투고 : 2018.02.08
  • 심사 : 2018.03.22
  • 발행 : 2018.06.25
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초록

Let R be a commutative ring with identity and let M be a finitely generated module over a Noetherian local ring R. Then it is well-known that M has a minimal projective resolution, which is unique up to isomorphisms of exact sequences. We provide a new proof of its uniqueness. Moreover, we deal with the cohomologies of (M, R/m).

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과제정보

연구 과제 주관 기관 : Sunchon National University

참고문헌

  1. M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969.
  2. Friedrich Ischebeck and Ravi A. Rao, Ideals and reality, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2005, Projective modules and number of generators of ideals, 2005.
  3. Satya Mandal, Projective modules and complete intersections, Lecture Notes in Mathematics, vol. 1672, Springer-Verlag, Berlin, 1997.
  4. Irena Swanson, Homological Algebra, Lecture Notes, Rome, Spring 2010.