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Paper   IPM / M / 531
School of Mathematics
  Title:   Grade and gorenstein dimension
  Author(s): 
1.  T. Sharif
2.  S. Yassemi
3.  L. Khatami
  Status:   Published
  Journal: Comm. Algebra
  No.:  11
  Vol.:  29
  Year:  2001
  Pages:   5085-5094
  Supported by:  IPM
  Abstract:
Let R be a commutative Noetherian ring and let M be a finite (that is, finitely generated) R-module. The notion grade of M, grade M, has been introduced by Rees as the least integer t ≥ 0 such that ExttR(M,R) ≠ 0, see [ 11]. The Gorenstein dimension of M, G−dimM, has been introduced by Auslander as the largest integer t ≥ 0 such that ExttR(M,R) ≠ 0, see [3]. In this paper the R-module M is called G-perfect if gradeM=G−dimM. It is a generalization of perfect module. We prove several results for the new concept similar to the classical results.

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