فهرست نشریات علمی دسترسی آزاد ایران

Let $R$ be a commutative Noetherian ring with non-zero identity, $\mathfrak{a}$ an ideal of $R$, $M$ a finitely generated $R$--module, and $a_1, \ldots, a_n$ an $\mathfrak{a}$--filter regular $M$--sequence. The formula\begin{align*}\operatorname{H}^i_\mathfrak{a}(M)\cong\left\{\begin{array}{lll}\operatorname{H}^i_{(a_1, \ldots, a_n)}(M) & \text{for all}\ \mathrm{i< n},\\\operatorname{H}^{i- n}_\mathfrak{a}(\operatorname{H}^n_{(a_1, \ldots, a_n)}(M)) & \text{for all}\ \mathrm{i\geq n},\end{array}\right.\end{align*}is known as Nagel-Schenzel formula and is a useful result to express the local cohomology modules in terms of filter regular sequences. In this paper, we provide an elementary proof to this formula.