Classification of split torsion torsionfree triples in module categories.
type: Item
instance of: scholarly article
title: Classification of split torsion torsionfree triples in module categories.
zbMATH Open document ID: 1121.16027
author: Pedro Nicolás
author: Manuel Saorín
published in: Journal of Pure and Applied Algebra
publication date: 2007-01-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0511159
review text: Let \(A\) be a ring with identity. A torsion torsionfree triple (a TTF-triple for short) in \(\text{Mod\,}A\) is a triple \((C,T,F)\) of three full subcategories in \(\text{Mod\,}A\) such that both \((C,T)\) and \((T,F)\) are torsion theories in \(\text{Mod\,}A\). A TTF-triple in \(\text{Mod\,}A\) is called left-split (resp. right-split) if the torion theory \((C,T)\) (resp. \((T,F)\)) splits. It is called centrally split if it is both left and right split. In this paper, in Section 2, the authors give the definitions and known results concerning TTF-triples in a module category. In Section 3, they give the classification of left-split TTF-triples in \(\text{Mod\,}A\). They present in Section 4 a partial classification of right-split TTF-triples. In Section 5, they classify the right-split TTF-triples \((C,T,F)\) in \(\text{Mod\,}A\) such that \(A_A\in F\), from which the classification of right-split TTF-triples follows.
Mathematics Subject Classification ID: 16S90
Mathematics Subject Classification ID: 18E40
Mathematics Subject Classification ID: 16D10
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 5083174
zbMATH Keywords: left-split TTF-triples
zbMATH Keywords: right-split TTF-triples
zbMATH Keywords: centrally split TTF-triples
zbMATH Keywords: torsion theories
zbMATH Keywords: categories of modules
reviewed by: Yoshiki Kurata
MaRDI profile type: Publication
OpenAlex ID: W2056916868
arXiv ID: math/0511159
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DOI: 10.1016/J.JPAA.2006.04.003
description: scientific article