A new lower bound for cohomological dimension

Let (R,\mathfrak{m}) be a Noetherian local ring, M a finitely generated R-module, and \mathfrak{a} an ideal of R. We define the \mathfrak{a}-minimum dimension d(\mathfrak{a},M) of M by d(\mathfrak{a},M)=Min\{\dim \frac{R}{\mathfrak{p}+\mathfrak{a}}:\mathfrak{p}\in Assh_{R}(M)\}. In this paper, we show that cd(\mathfrak{a},M)\geq \dim M-d(\mathfrak{a},M) and we give some sufficient conditions and characterization for the equality to hold true.

کلیدواژه ها:

Local cohomology ، cohomological dimension ، cofinite modules