“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 9493
School of Mathematics
  Title:   Artinian and non-artinian local cohomology modules
  Author(s):  M. T. Dibaei (Joint with A. Vahidi)
  Status:   Published
  Journal: Canad. Math. Bull.
  Vol.:  54
  Year:  2011
  Pages:   619-629
  Supported by:  IPM
Let M be a finite module over a commutative noetherian ring R. For ideals \fa and \fb of R, the relations between cohomological dimensions of M with respect to \fa, \fb, \fa∩\fb and \fa+ \fb are studied. When R is local, it is shown that M is generalized Cohen-Macaulay if there exists an ideal \fa such that all local cohomology modules of M with respect to \fa have finite lengths. Also, when r is an integer such that 0 ≤ r < dimR(M), any maximal element \fq of the non-empty set of ideals {\fa : \"\fai(M) is not artinian for some i, ir} is a prime ideal and that all Bass numbers of \"\fqi(M) are finite for all ir.

Download TeX format
back to top
scroll left or right