Universal co-Extensions of torsion abelian groups

Alejandro Argudín-Monroy; Carlos E. Parra

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arXiv · 2206.08857

Universal co-Extensions of torsion abelian groups

Alejandro Argudín-Monroy·Carlos E. Parra

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Abstract

In [16], a theory of universal extensions in abelian categories is developed; in particular, the notion of Ext-universal object is presented. In the present paper, we show that an Ab3 abelian category which is Ext-small satisfies the Ab4 condition if, and only if, each one of its objects is Ext-universal. We also give a characterization of the co-Ext-universal objects of the category of torsion abelian groups. In particular, we show that such groups are the ones admitting a decomposition $Q\oplus R$, in which $Q$ is injective and $R$ is a reduced group on which each $p$-component is bounded.

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BibTeX RIS

Alejandro Argudín-Monroy, Carlos E. Parra. 2022-06-17. Universal co-Extensions of torsion abelian groups. https://arxiv.org/abs/2206.08857

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