Uma introdução ao funtor Tor

Abstract

This work aims to study the functor Tor, an tool important in homological algebra and algebraic geometry. The functor T orA n (M, N) measures the failure of the tensor product to preserve exactness, revealing information about the structure of the involved modules. To achieve this, the work is divided into three chapters. The first presents preliminar concepts such as A-modules, exact sequences, and the Snake Lemma. The second chapter discusses the construction of the tensor product, highlighting its exactness property. In the third chapter, the Tor functor is studied from a projective resolution and the homology of the tensorized complex, also discussing its main properties and applications.