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Paper   IPM / M / 8423
School of Mathematics
  Title:   Associated and attached primes of some graded modules over semigroup rings
1.  H. Sabzrou
2.  M. Tousi
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  35
  Year:  2007
  Pages:   2793-2809
  Supported by:  IPM
In Helm and Miller (2003, Section 8), the authors posed the problem of which faces of a saturated affine semigroup Q correspond to prime ideals associated to the local cohomology module HiIR) where ωR is the canonical module of the semigroup ring R = k[Q], k a field, and I is a monomial ideal in R. In this paper we will give a solution in the case that Q is simplicial. We will also consider a similar problem for attached primes of the local cohomology module Him(M) where M is a squarefree module (in sense of Definition 2.7) and m is the homogeneous maximal ideal of R. As a result, we will show that for a squarefree monomial ideal I in a normal simplicial semigroup ring R and each integer i ≥ 0, we have Ass HiIR) = Att Hdim(R/ I) where d= dim R.

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