Sobre Tor-rigidez e profundidade de produtos tensoriais de módulos

Abstract

In this dissertation, after presenting some preliminary results from commutative algebra, we concentrate ourselves in the study of the so-called Tor rigidity problem, as well as the depth formula for the tensor product of modules and some results about freeness. Applying some of the facts presented in this work, we obtain, as one of the main corollaries, that for appropriate modules M, N over a hypersurface ring R satisfying the property that M⊗RN is reflexive, the following formula (proved originally by C. Huneke and R. Wiegand) is valid:

depth(M ⊗R N) = depth(M) + depth(N) − dim(R).