Aspects of Free Actions Based on Dependent Elements in Group Rings
Open Access
- 21 June 2022
- journal article
- Published by Earthline Publishers in Earthline Journal of Mathematical Sciences
- Vol. 10 (1), 183-193
- https://doi.org/10.34198/ejms.10122.183193
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.Keywords
This publication has 12 references indexed in Scilit:
- Derivation Algebra in Noncommutative Group AlgebrasProceedings of the Steklov Institute of Mathematics, 2020
- Derivations of group ringsActa Scientiarum Mathematicarum, 2020
- Complex of n-categories and derivations in group algebrasTopology and its Applications, 2019
- (σ,τ)-Derivations of group ringsCommunications in Algebra, 2019
- Derivation rings of Lie ringsSão Paulo Journal of Mathematical Sciences, 2017
- The group of automorphisms of the Lie algebra of derivations of a polynomial algebraJournal of Algebra and Its Applications, 2017
- A Note on Derivations of Group RingsCanadian Mathematical Bulletin, 1995
- Derivations of integral group ringsCommunications in Algebra, 1994
- Advances in group ringsIsrael Journal of Mathematics, 1974
- Primitive group ringsPacific Journal of Mathematics, 1973