论文标题
关于霍普夫（共依恋）和安装S-cActs（i）
On Hopfian(co-Hopfian) and Fitting S-acts (I)
论文作者
论文摘要
本工作的主要目的是对霍普夫（Hopfian）（共求人）行为的调查，其表现性（注射性）内态性是同构。尽管我们研究了与这些类别的行为相关的条件，但研究了它们与其他一些概念的相互关系，例如准文化和dedekind-finite行为。使用Hopfian和Co-Hopfian概念，给出了几种条件，以进行准文化行为。此外，我们带来了一些强烈的Hopfian和强烈共同共同$ S $ $的物业。最终，我们介绍并研究了拟合行为的概念，并且在单型$ s $上，发现某些等效条件具有所有有限生成的（循环）的作用。结果表明，只有当它既是强烈的Hopfian又有强烈的共同投资人时，就可以合适。
The main purpose of the present work is an investigation of the notions Hopfian (co-Hopfian) acts whose their surjective (injective) endomorphisms are isomorphisms. While we investigate conditions that are relevant to these classes of acts, their interrelationship with some other concepts for example quasi-injective and Dedekind-finite acts is studied. Using Hopfian and co-Hopfian concepts, several conditions are given for a quasi-injective act to be Dedekind-finite. Moreover we bring out some properties of strongly Hopfian and strongly co-Hopfian $S$-acts. Ultimately we introduce and study the concept of Fitting acts and over a monoid $S$, some equivalent conditions are found to have all its finitely generated (cyclic) acts Fitting. It is shown that an $S$-act is Fitting if and only if it is both strongly Hopfian and strongly co-Hopfian.
