Properties Of The Pinched Tensor Product

Abstract

For complexes of modules we study a new construction, called the pinched tensor product, which was introduced by Lars Winther Christensen and David A. Jorgensen to study Tate homology. We explore properties of the pinched tensor product and their comparison to properties of the ordinary tensor product. For example; we show some isomorphisms no longer holds for the pinched tensor product. Although if we change isomorphism to quasi-isomorphism the pinched version holds. Plus if f is a map from C to D and g is a map from A to B are morphisms of complexes of R-modules with f homotopic to 0, then the tensor map between f and g also homotopic to 0, and this property is not true for the pinched tensor product.