On Some Kinds of Injectivity of GHS-Acts

In the theory of S-acts, there exists a plethora of compelling findings that establish connections between regularity in a monoid S and injectivity (as well as other notions derived from injectivity) of Sacts. In this paper, we introduce the notion of strongly regular elements in a hypermonoid as a generalization of regular elements in a monoid and extend several classic results to hypermonoids and GHS-acts over hypermonoids. Particularly, we show that a hypermonoid S is strongly regular and injective GHS-act if and only if all right hyperideals of S are C-injective.