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On Differential Torsion Theories and Rings with Several Objects
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 62 / Issue 4 / December 2019
- Published online by Cambridge University Press:
- 08 April 2019, pp. 703-714
- Print publication:
- December 2019
-
- Article
- Export citation
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Let
${\mathcal{R}}$ be a small preadditive category, viewed as a “ring with several objects.” A right
${\mathcal{R}}$-module is an additive functor from 
${\mathcal{R}}^{\text{op}}$ to the category 
$Ab$ of abelian groups. We show that every hereditary torsion theory on the category 
$({\mathcal{R}}^{\text{op}},Ab)$ of right 
${\mathcal{R}}$-modules must be differential.
