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On Differential Torsion Theories and Rings with Several Objects

Part of: Rings and algebras arising under various constructions Abelian categories

Published online by Cambridge University Press:  08 April 2019

Abhishek Banerjee
Abhishek Banerjee*
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore-560012, India Email: [email protected]
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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.

Keywords

hereditary torsion theorydifferential torsion theoryring with several objects

MSC classification

Primary: 16S90: Torsion theories; radicals on module categories
Secondary: 18E05: Preadditive, additive categories 18E40: Torsion theories, radicals
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 4 , December 2019 , pp. 703 - 714
Copyright
© Canadian Mathematical Society 2019 

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