%0 Journal Article
%T On C-injective generalized hyper S-acts
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Ghasempour, Maedeh
%A Rasouli, Hamid
%A Iranmanesh, Ali
%A Barzegar, Hasan
%A Tehranian, Abolfazl
%D 2023
%\ 08/01/2023
%V 19
%N 1
%P 127-141
%! On C-injective generalized hyper S-acts
%K hypermonoid
%K generalized hyper S-act
%K Injectivity
%K C-injectivity
%K semi-injectivity
%R 10.48308/cgasa.19.1.127
%X 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.
%U https://cgasa.sbu.ac.ir/article_103881_92769525788a374436c796f5305133ba.pdf