Questions tagged [torsion-theory]

Let $\mathcal{A}$ be an abelian category. In the context of my work I am considering pairs of ideals $(\mathcal{I}, \mathcal{J})$ in $\mathcal{A}$ with the following properties: $\quad \mathcal{I} \...

Let $\mathcal{A}$ be a length abelian category. A subclass $\mathcal{S}$ of $\mathcal{A}$ is called super-closed if $0\in \mathcal{S}$, $\mathcal{S}$ is closed under extensions and $\mathcal{A}\...

I'm looking for intuition and references for the definition of a hereditary torsion theory and two facts found here. First, the definition and facts: Definition. A torsion theory $(\mathcal T,\...

Let $\mathscr{I}_\sigma$ be the Gabriel filter of ideals for a hereditary torsion theory $\sigma$ over a commutative ring $R$. I am looking for equivalent conditions on either $\sigma$ or $R$ under ...