On generalization of hollow acts
Shaymaa Amer Abdul-Kareem, Ahmed A. Abdulkareem · AIP conference proceedings · 2022
In this paper, we introduced a generalization of the hollow act which is known as hollow-lifting act and obtained new properties and characterizations for this notion. It is known that a unitary right S-act A over S which is denoted by AS could be a non-empty set with a function f ∶ A × S ⟶ A specified f(a, s) ⟼ as and also the following properties hold: (1) a•1=a. (2) a(st) = (as)t for all a ∈ A and s, t ∈ S. An S-act MS is stated as hollow-lifting if every subact N of MS such that MS/N is hollow includes a coessential subact that is a retract subact of MS. Conditions under which subacts are inheriting the property of the Hollow-lifting act are examined. The relationship between hollow acts and hollow-lifting is taken into account. Ultimately, the notion of the indecomposable act is employed to coincide with these classes. The conclusion of our work is clarified within the last section.