论文标题
扭转扭转阿贝尔群
Universal co-Extensions of torsion abelian groups
论文作者
论文摘要
在[16]中，开发了阿贝尔类别中普遍扩展的理论。特别是，提出了末期对象的概念。在本文中，我们显示出一个AB3 ABELIAN类别是Ext-Mall的AB3 Abelian类别，并且只有当它的每个对象都是Ext-Umiversal时，就可以满足AB4条件。我们还给出了扭转阿伯利亚群体类别的共同ext-宇宙对象的特征。特别是，我们表明这样的组是承认分解$ q \ oplus r $的组，其中$ q $是注入性的，$ r $是一个减少的组，每个$ p $ - 组件都被限制。
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.
