On C-injective generalized hyper S-acts | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 7، دوره 19، شماره 1، آبان 2023، صفحه 127-141 اصل مقاله (471.6 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.48308/cgasa.19.1.127 | ||
| نویسندگان | ||
| Maedeh Ghasempour1؛ Hamid Rasouli* 2؛ Ali Iranmanesh3؛ Hasan Barzegar4؛ Abolfazl Tehranian1 | ||
| 1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran | ||
| 2Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran | ||
| 3Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran | ||
| 4Department of Mathematics, Tafresh University, Tafresh 39518- 79611, 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 all inclusions from cyclic GHS-subacts into indecomposable ones. Then we introduce new 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 be classified as semi-injective. | ||
| کلیدواژهها | ||
| hypermonoid؛ generalized hyper S-act؛ injectivity؛ C-injectivity؛ semi-injectivity | ||
| مراجع | ||
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