Identities related to left generalized derivations in near-rings

In this paper, we studied commutative near-rings through identities involving a mapping known as the left generalized derivation. Our results generalize several well-known findings in the literature, including those in references [M. Ashraf and A. Boua, Identities in [Formula: see text]-prime near-rings with left multipliers, J. Algebra Relat. Topics 6(1) (2018) 67–77; A. Boua, Some identities in [Formula: see text]-prime near-rings with derivations, Commun. Korean Math. Soc. 40(1) (2025) 27–37], and they also make significant contributions to the existing body of research in this area. Furthermore, this paper provides examples that illustrate the necessity of the assumptions underlying our results.