We introduce and study (strongly) π-Rickart objects and their duals in abelian categories, which generalize (strongly) self-Rickart objects and their duals. We establish general properties of such objects, we analyze their behavior with respect to coproducts, and we study classes all of whose objects are (strongly) π-Rickart. We derive consequences for module and comodule categories.

中文翻译：

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阿贝尔范畴中的 π-Rickart 和对偶 π-Rickart 对象

我们介绍和研究（强烈）π-Rickart 对象及其在阿贝尔类别中的对偶，它（强烈）概括了自 Rickart 对象及其对偶。我们建立这些对象的一般属性，我们分析它们关于副产品的行为，我们研究所有对象的类（强烈）π-里卡特。我们推导出模块和协模块类别的结果。