@article{Mahmood_2022, title={Aspects of Free Actions Based on Dependent Elements in Group Rings}, volume={10}, url={https://earthlinepublishers.com/index.php/ejms/article/view/539}, DOI={10.34198/ejms.10122.183193}, abstractNote={<p>This paper contains two directions of work. The first one gives material related to free action (an inner derivation) mappings on a group ring R[G] which is a construction involving a group G and a ring R and the dependent elements related to those mappings in R[G]. The other direction deals with a generalization of the definition of dependent elements and free actions. We concentrate our study on dependent elements, free action mappings and those which satisfy T(x)γ=δx,x∈R[G] and some fixed γ,δ∈R[G]. In the first part we work with one dependent element. In other words, there exists an element γ∈R[G] such that T(x)γ=γx,x∈R[G]. In second one, we characterize the two elements γ,δ∈R[G] which have the property T(x)γ=δx,x∈R[G] and some fixed γ,δ∈R[G], when T is assumed to have additional properties like generalized a derivation mappings.</p>}, number={1}, journal={Earthline Journal of Mathematical Sciences}, author={Mahmood, Sahar Jaafar}, year={2022}, month={Jun.}, pages={183-193} }