In this paper, we introduce the concept of Baer (p,q)-sets. Using this notion, we define Rickart, Baer, quasi-Baer and π-Baer (S,R)-bimodules, respectively. We show how these conditions relate to each other. We also develop new properties of the minus binary relation, ≤-, we extend the relation ≤- to (S,R)-bimodules and use it to characterize the aforementioned Rickart, Baer, quasi-Baer, and π-Baer (S,R)-bimodules. Moreover, we specify subsets 𝒦 of the power set of a (S,R)-bimodule for which ≤- determines a partial order and for which ≤- is a lattice. We analyze the relation ≤- by examining the associated Baer (p,q)-sets. Finally, we apply our results to C∗-modules. Examples are provided to illustrate and delimit our results.

中文翻译：

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Baer 双模子集的偏序及其对 C∗-模的应用

在本文中，我们介绍了 Baer 的概念(p,q)-套。使用这个概念，我们定义了 Rickart、Baer、quasi-Baer 和π-贝尔(小号,R)-双模块，分别。我们展示了这些条件如何相互关联。我们还开发了负二元关系的新属性， ≤-，我们扩展关系 ≤- 到(小号,R)-bimodules 并用它来表征前面提到的 Rickart、Baer、quasi-Baer 和π-贝尔(小号,R)-双模块。此外，我们指定子集𝒦的幂集(小号,R)-bimodule 为其 ≤- 确定一个偏序，并为其 ≤- 是一个格子。我们分析关系 ≤- 通过检查相关的 Baer(p,q)-套。最后，我们将结果应用于C*-模块。提供示例来说明和界定我们的结果。