The finiteness of coassociated primes of generalized local homology modules

Abstract

We present some finiteness results for co-associated primes of generalized local homology modules. Let M be a finitely generated R-module and N a linearly compact R-module. If N and HiI (N) satisfy the finiteness condition for co-associated primes for all i < k, then CoassR(HkI (M,N)) is a finite set. On the other hand, if HiI (N) = 0 for all i < t and TorjR (M,Hti (N)) = 0 for all j < h, then TorhR (M,HtI (N)) ≅ Hh+tI(M,N). Moreover, Coass(Hh+tI(M,N)) is also a finite set providedN satisfies the finiteness condition for co-associated primes. Finally, N is a semi-discrete linearly compact R-module such that 0:NI ≠ 0. Let t=WidthI (N) and h = tor_(M,HtI (N)); it follows that WidthI+Ann(M)(N) = t + h and Coass(Hh+tI(M,N)) is a finite set.