Aspects of Free Actions Based on Dependent Elements in Group Rings

• Sahar Jaafar Mahmood Department of Multimedia, College of Computer Science and Information Technology, University of AlQadisiyah, P.O. Box 88, Al Diwaniyah, Al-Qadisiyah, Iraq
Keywords: group ring, inner derivations, prime group rings, dependent elements, free action

Abstract

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.

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Published
2022-06-21
How to Cite
Mahmood, S. J. (2022). Aspects of Free Actions Based on Dependent Elements in Group Rings. Earthline Journal of Mathematical Sciences, 10(1), 183-193. https://doi.org/10.34198/ejms.10122.183193
Section
Articles