The notion of weakly injective \( S \)-act can be regarded as a generalization of the notion of injective \( S \)-act. This article describes the finite monoids over which each weakly injective \( S \)-act has a primitively normal theory. Moreover, we show that the primitive normality of the class of all principally weakly injective \( S \)-acts is equivalent to \( S \) being totally ordered.

中文翻译：

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一类弱注入 S-Acts 的原始正态性

弱内射\（S \）- act的概念可以看作是内射\\（S \）- act的概念的 概括。本文描述了有限幺半群，每个弱单射\( S \) -act 都有一个原始正规理论。此外，我们证明了所有主要弱单射\( S \) -acts的类的原始正态性等价于 \( S \) 是完全有序的。