Vanishing and localization of (d,\frak{b})-ideal transforms

Let R be a commutative Noetherian ring, \!M an \!R-module and d a non-negative integer. Let \Sigma denote the set of ideals \frak{I} of R such that \mathrm{dim}(R/\frak{I})\!\leq\!d. For an ideal \frak{b} of R, we define the (d,\i\frak{b})-transform D_{d,\i\i\frak{b}}(M) and study its properties. Then a criterion for D_{d,\frak{b}}(R)\!=\!\bigcap_{\frak{p}\notin W(d,\frak{b})}R_{\frak{p}} will be given, where W(d,\frak{b}) contains all ideals \frak{a} of R such that \frak{I}\subseteq \frak{a}+\frak{b} for some \frak{I}\in \Sigma. For each i\geq ۰, let D^i_{d,\frak{b}}(-) denote the i-th right derived functor of D_{d,\frak{b}}(M). We study the localization of the module D^i_{d,\frak{b}}(M) and prove that  D^i_{d,\frak{b}}(M)_\frak{p}\cong D^i_{d-\textrm{dim}(R/(\frak{p}+\frak{b})),\frak{b}_\frak{p}}(M_\frak{p}) for all \frak{p}\in\mathrm{Spec}(R) and all i\geq ۰. Finally, we establish vanishing theorems for D^i_{d,\frak{b}}(M).

کلیدواژه ها:

local cohomology ، ideal transforms ، finitely generated ، localization ، associated prime