A study of absolute, relative and Tate homology with respect to a semidualizing module

In this paper we are concerned with absolute, relative and Tate Tor modules with respect to a fixed semidualizing module over commutative Noetherian local rings. Motivated by a result of Avramov and Martsinkovsky, we obtain an exact sequence connecting absolute Tors with relative and Tate Tors. As a consequence, we prove results that relate the vanishing of Tor modules to the depth of tensor products, and extend a result of Auslander in this direction.

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