In this paper, the s.Baer module concept and some of its generalizations (e.g. quasi-s.Baer, π-s.Baer and p.q.-s.Baer) are developed. To this end, we characterize the class of rings for which every module is quasi-s.Baer as the class of rings which are finite direct sums of simple rings. Connections are made between the s.Baer (quasi-s.Baer, π-s.Baer) and the extending (FI-extending, π-extending) properties. We introduce the notions of quasi-nonsingularity (FI-s.nonsingular, π-s.nonsingular) and M-cononsingular (FI-M-cononsingular, π-M-cononsingular) to extend the Chatters–Khuri theorem from rings to modules satisfying s.Baer or related conditions. Moreover, we investigate the transfer of various Baer properties between a module and its ring of scalars. Conditions are found for which some classes of quasi-s.Baer modules coincide with some classes of p.q.-s.Baer modules. Further we show that the class of quasi-s.Baer (p.q.-s.Baer) modules is closed with respect to submodules, extensions, and finite (arbitrary) direct sums. Examples illustrate and delimit our results.

中文翻译：

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准s.Baer及相关模块

在本文中，s.Baer 模块概念及其一些推广（例如 quasi-s.Baer，π-s.Baer 和 pq-s.Baer) 被开发。为此，我们将每个模都是准s.Baer的环类描述为简单环的有限直和的环类。s.Baer (quasi-s.Baer,π-s.Baer) 和扩展 (FI-extending,π-扩展）属性。我们引入准非奇异性的概念（FI-s.nonsingular，π-s.nonsingular) 和米-cononsingular (FI-米-consingular,π-米-cononsingular) 将 Chatters-Khuri 定理从环扩展到满足 s.Baer 或相关条件的模块。此外，我们研究了模块及其标量环之间各种 Baer 属性的传递。找到准s.Baer模块的某些类与pq-s.Baer模块的某些类重合的条件。此外，我们表明准s.Baer (pq-s.Baer) 模块的类在子模块、扩展和有限（任意）直接和方面是封闭的。示例说明并界定了我们的结果。