On Some Kinds of Injectivity of GHS-Acts
Abstract
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 extends several classic results to hypermonoids and GHS-acts over
hypermonoids. Particularly, we show that S is strongly regular and
injective GHS-act if and only if all right ideals of S are C-injective.
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 extends several classic results to hypermonoids and GHS-acts over
hypermonoids. Particularly, we show that S is strongly regular and
injective GHS-act if and only if all right ideals of S are C-injective.
Keywords
hypermonoid; generalized hyper $S$-act; $W$-injectivity; $PW$-injectivity; $C$-injectivity; strong regularity
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