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Paper   IPM / M / 532
School of Mathematics
  Title:   A generalization of the grade of a module
1.  S. Yassemi
2.  L. Khatami
3.  T. Sharif
  Status:   Published
  Journal: Algebra Colloq.
  No.:  3
  Vol.:  9
  Year:  2002
  Pages:   265-270
  Supported by:  IPM
Let R be a commutative Noetherian ring and let M be a finite (i.e., finitely generated) R-module. The grade of M was introduced by Rees as the least integer l ≥ 0 such that ExtlR(M,R) ≠ 0. It is well known that the grade of M is the least integer l ≥ 0 such that Extl(M,P) ≠ 0 for some projective module P. In this paper, we study the least integer l ≥ 0 such that Extl(M,F) ≠ 0 for some flat R-module F when M is not necessarily finite. This is an extension of the grade of M. Similar to the classical results, we prove several results for the new concept.

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