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Classification of split torsion torsionfree triples in module categories

Pedro Nicolas·Manuel Saorin
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Abstract

A TTF-triple $(\mathcal{C},\mathcal{T},\mathcal{F})$ in an abelian category is called 'one-sided split' in case either $(\mathcal{C},\mathcal{T})$ or $(\mathcal{T},\mathcal{F})$ is a split torsion theory. In this paper we classify one-sided split TTF-triples in module categories, thus completing Jans' classification of two-sided split TTF-triples and answering a question that has remained open for almost forty years.

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Pedro Nicolas, Manuel Saorin. 2005-11-07. Classification of split torsion torsionfree triples in module categories. https://arxiv.org/abs/math/0511159

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