We deal with questions concerning the completeness and stability of a class of injective acts and a class of weakly injective acts over a monoid S. The concepts of an injective S-act and of a weakly injective S-act are analogs of the concept of an injective module. In the theory of modules, the corresponding notions of injectivities in accordance with Baer’s criterion coincide. Also we will look into the completeness and stability of a class of principally weakly injective S-acts and a class of fg-weakly injective S-acts, which are analogs of p-injective modules and finitely injective modules.

中文翻译：

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内射S-行为类的完备性和稳定性。

我们处理有关在类半群S上的一类内射性行为和一类弱内射性行为的完整性和稳定性的问题。内射性S-act和弱内射性S-act的概念与内射模块。在模块理论中，按照Baer准则的相应的内射性概念是一致的。我们还将研究一类主要是弱内射S-动作和一类fg-弱内射S-动作的完整性和稳定性，它们是p-内射模和有限内射模的类似物。