  This paper main goal is to measure the defect of Cohen-Macaulayness,
Gorensteiness, complete intersection and regularity for the tensor product of
algebras over a ring. For this sake, we determine the homological invariants
which are inherent to these notions, such as the Krull dimension, depth,
injective dimension, type and embedding dimension of the tensor product
constructions in terms of those of their components.
