The theory of local homology for Artinian modules (Q1586833)

The authors develop the theory of local homology for an Artinian module \(A\) over a commutative ring \(R\) with identity with respect to the following concepts: Starting from an ideal \({\mathfrak a}\subset R\) and its \({\mathfrak a}\)-adic completion functor the authors study \({\mathfrak a}\)-cotorsion modules and \({\mathfrak a}\)-cotorsion-free modules under the Matlis duality functor and give conditions on \(R\) and \(A\) such that the zero submodule of the local homology module \(H_i^{\mathfrak a}(A)\) has a primary decomposition. Moreover they introduce the dual of the ideal transform functor and obtain some results analogous to those of the ideal transform functor.