Associated primes of local cohomology and S-2-ification

作者：Robbins Hannah^*

来源：Journal of Pure and Applied Algebra, 2012, 216(3): 519-523.

DOI：10.1016/j.jpaa.2011.06.011

Let R be commutative Noetherian, I subset of R an ideal, and M a finitely generated R-module. We prove that if R/P has an S-2-ification for all P is an element of Spec(R) then the set of primes associated to the second local cohomology module H-I(2)(M) is finite when ht(IR/P) %26gt;= 2 for all P is an element of Ass(R)M and Ass(R)M subset of Ass(R)R. We use that to show that if dim(R) = 3 and the ideal transform of R with respect to any height 2 ideal generated by non-zerodivisors is a finitely generated module, then Ass(R)H(I)(i)(M) is finite for any I with ht (IR/P) %26gt;= 2. We also reduce the problem of showing Ass(R)H(I)(i)(M) is finite for local four dimensional rings to an extremely concrete case.

• 出版日期2012-3