If two torsion theories on a ring localize the ring to the same extension ring, I can find no reason that their "meet" in the lattice of torsion theories must also localize to the …

I need to discuss torsion-free sheaves on reduced, but possibly reducible spaces. Here "torsion" means "element is annihilated by a non-zero-divisor". The standard references (EGA, …

Let me start saying that a similar question can be stated for general locally Noetherian Grothendieck categories but I state it for categories of rings as it is simpler. So we fix …

I want example for a hereditary torsion pair,can you help me?

I am away from Torsion theory in abelian category for some while. So It might be a stupid question. The definition of torsion pair in category of modules is as follows: Definiti …

I am looking for reference talking about how torsion theory play roles in algebraic geometry. I will be really happy to see some concrete examples. Say, talking about torsion theor …