graduation at Bacharelado em Matematica from Universidad Nacional Pedro Ruiz Gallo (2019). Has experience in Mathematics, focusing on Algebra (Source: Lattes Curriculum)
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Let $R$ be a commutative Noetherian ring with unity and $M$ be a finitely generated $R$-module. It is know that if each finitely generated $R$-module $N$ satisfies the condition that the $R$-module $\mbox{Ext}^{i}_R(M,N)$ is the zero module for every integer $i>0$, then $M$ is projective. A question that arises is the following: if such condition holds at least for $N=R$ and $N=M$, is it …
This project aims to investigate the implications of the vanishing of Ext and Tor. One of its objectives is to establish criteria for the freeness of a module over a Noetherian local ring through the vanishing of specific Ext or Tor modules. Special attention is dedicated to cases where the Hom or the tensor product of two particular modules has some finite homological dimension.
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