Bulletin of the
Korean Mathematical Society BKMS

Let $A$ be Noetherian ring, $\fa=(r_1,\dots,r_n)$ an ideal of $A$ and $\mathcal C_A$ be category of $A$-modules and $A$-homomorphisms. We show that the connected left sequences of covariant functors $\{\underset{t\in\BN}{\vpl} H_i(K_\bullet(\fr^t,-))\}_{i\geq 0}$ and $\{\underset{t\in\BN}{\vpl}\Tor_i^A(\frac{A}{\fa^t},-)\}_{i\geq 0}$ are isomorphic {\linebreak}from $\mathcal C_A$ to itself, where $\fr^t=r_1^t,\dots,r_n^t$.

Keywords: local homology modules, Koszul complex, Noetherian ring, inverse limit, completion

MSC numbers: 13D07, 13D25, 13E05