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Purely Rickart and Dual Purely Rickart Objects in Grothendieck Categories
Mediterranean Journal of Mathematics ( IF 1.1 ) Pub Date : 2021-09-07 , DOI: 10.1007/s00009-021-01859-6
Sultan Eylem Toksoy 1
Affiliation  

In this paper, (dual) purely Rickart objects are introduced as generalizations of (dual) Rickart objects in Grothendieck categories. Examples showing the relations between (dual) relative Rickart objects and (dual) relative purely Rickart objects are given. It is shown that in a spectral category, (dual) relative purely Rickart objects coincide with (dual) relative Rickart objects. (Co)products of (dual) relative purely Rickart objects are studied. Classes all of whose objects are (dual) relative purely Rickart are identified. It is shown how this theory may be employed to study (dual) relative purely Baer objects in Grothendieck categories. Also applications to module and comodule categories are given.



中文翻译:

格罗腾迪克类别中的 Purely Rickart 和 Dual Purely Rickart 对象

在本文中,(双)纯 Rickart 对象被介绍为格洛腾迪克范畴中(双)Rickart 对象的推广。给出了显示(双)相对 Rickart 对象和(双)相对纯 Rickart 对象之间关系的示例。结果表明,在一个光谱范畴中,(双)相对纯瑞卡天体与(双)相对瑞卡天体重合。研究了(双)相对纯 Rickart 对象的(共)积。标识所有对象都是(双重)相对纯粹 Rickart 的类。展示了如何使用该理论来研究格洛腾迪克范畴中的(双重)相对纯 Baer 对象。还给出了模块和协模块类别的应用。

更新日期:2021-09-08
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