TY - JOUR
AU - Sahar Jaafar Mahmood
PY - 2022/06/21
Y2 - 2022/08/07
TI - Aspects of Free Actions Based on Dependent Elements in Group Rings
JF - Earthline Journal of Mathematical Sciences
JA - EJMS
VL - 10
IS - 1
SE - Articles
DO - 10.34198/ejms.10122.183193
UR - https://earthlinepublishers.com/index.php/ejms/article/view/539
AB - 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.
ER -