On C-injective generalized hyper S-acts
- سال انتشار: 1402
- محل انتشار: مجله نظریه رسته ها و ساختارهای کلی جبری با کاربردها، دوره: 19، شماره: 1
- کد COI اختصاصی: JR_CGASAT-19-1_006
- زبان مقاله: انگلیسی
- تعداد مشاهده: 155
نویسندگان
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
Department of Mathematics, Tafresh University, Tafresh ۳۹۵۱۸- ۷۹۶۱۱, Iran
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
چکیده
This paper explores generalized hyper S-acts (GHS-acts) over a hypermonoid S as generalizations of monoid acts within the context of algebraic hyperstructures. Specifically, we extend the definition of C-injectivity to GHS-acts and investigate their internal and homological properties. It is established that for being GHS-injectivity of GHS-acts with a fixed element, it suffices to consider allinclusions from cyclic GHS-subacts into indecomposable ones. Then we introducenew concepts known as semi-injectivity and semi-C-injectivity. By providing examples, we demonstrate that injectivity and semi-injectivity (C-injectivity and semiC-injectivity) are different concepts for GHS-acts, whereas they are the same in the context of acts over monoids. It is also shown that all pure GHS-acts are injective if and only if all pure cyclic GHS-acts are C-injective. Furthermore, we establish an equivalent condition on a hypermonoid S such that all quotients of SS exhibit semi-injectivity. Finally, we derive an equivalent condition for a hypermonoid to beclassified as semi-injective.کلیدواژه ها
hypermonoid, generalized hyper S-act, Injectivity, C-injectivity, semi-injectivityاطلاعات بیشتر در مورد COI
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