A NOTE ON THE LOCAL HOMOLOGY

Abstract

Let A be Noetherian ring, a= (<TEX>${\tau}_1..., \tau_n$</TEX> an ideal of A and <TEX>$C_{A}$</TEX> be category of A-modules and A-homomorphisms. We show that the connected left sequences of covariant functors <TEX>${limH_i(K.(t^t,-))}_{i\geq0}$</TEX> and <TEX>${lim{{Tor^A}_i}(\frac{A}{a^f}-)}_{i\geq0}$</TEX> are isomorphic from <TEX>$C_A$</TEX> to itself, where <TEX>$\tau^t\;=\;{{\tau_^t}_1$</TEX>, ㆍㆍㆍ<TEX>${\tau^t}_n$</TEX>.