On the finiteness of co-associated primes of local homology modules
Let \(R\) be a commutative noetherian ring. A topological \(R\)-module \(M\) is called linearly topologized if its zero element has a base of neighborhoods consisting of open submodules. Also a Hausdorff linearly topologized \(R\)-module \(M\) is said to be linearly compact if \(F\) is a family of closed cosets in \(M\) which has the finite intersection property, then the cosets in \(F\) have a nonempty intersection. Assume that \(M\) is linearly compact. Let \(I\) be an ideal of \(R\) and \(i\) a non-negative integer. This paper provides some finiteness results for the set of coassociated prime ideals of the local homology module \(H_i^{I}(M)\) defined via the inverse limit of the inverse system \(\mathrm{Tor}_i ^R (R/ I^n, M)\). More precisely, \(H_s^{I}(M)\) has finitely many coassociated prime ideals, if \(M\) and \(H_i^{I}(M)\) have finitely many coassociated prime ideals for all \(i<s\).
scientific article; zbMATH DE number 5568609
scientific article