On Centrally Extended Generalized \(*\) -Homoderivations in Rings with Involution
摘要
The aim of the present paper is to establish significant results in the realm of centrally extended \( * \) -homoderivations and centrally extended generalized \( * \) -homoderivations in a ring \(\mathfrak {S}\) with involution. Within this framework, we provide examples of mappings that possess the property of being centrally extended \(*\) -homoderivations, but not of \(*\) -homoderivations. Our investigation delves into the intricate interplay between these mappings and their influence on the center of the ring denoted as \( Z(\mathfrak {S}) \) .