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On Differential Torsion Theories and Rings with Several Objects

Published online by Cambridge University Press:  08 April 2019

Abhishek Banerjee*
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore-560012, India Email: abhishekbanerjee1313@gmail.com

Abstract

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.

Type
Article
Copyright
© Canadian Mathematical Society 2019 

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