SOME RESULTS ON THE 0TH FORMAL LOCAL COHOMOLOGY WITH RESPECT TO A NON-MAXIMAL IDEAL

Abstract

This paper studies the formal local cohomology with respect to non-maximal ideals. It is an extension of the formal local cohomology for maximal ideals by Schenzel (2007). By using the properties of inverse limits and I-adic topology, we have proved several crucial properties of the formal local cohomology of order 0 regarding non-maximal ideals. In particular, detailed computations were provided for the local cohomology of order 0 as regards non-maximal ideals. The equivalent properties of the formal local cohomology of order 0 regarding non-maximal ideals and associated primes of modules are rigorously proven.