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Paper   IPM / M / 8010
School of Mathematics
  Title:   Characterizing local rings via homological dimensions and regular sequences
1.  Sh. Salarian
2.  S. Yassemi (Joint with S. Sather-Wagstaff)
  Status:   Published
  Journal: J. Pure Appl. Algebra
  Vol.:  207
  Year:  2006
  Pages:   99-108
  Supported by:  IPM
Let (R, \frak m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If GC-dimension of M/\fraka M is finite for all ideals \frak a generated by an R-regular sequence of length at most dt then either GC-dimension of M is at most t or C is a dualizing complex. Analogous results for other homological dimensions are also given.

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