Derivations of group rings

Artemovych, Orest D.; Bovdi, Victor; Salim, Mohamed

doi:10.14232/actasm-019-664-x

Cited by 8 publications

(2 citation statements)

References 34 publications

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“…In recent papers [16,17,18,19,20,21,22], properties of generalized derivations, central derivations and derivations of group rings over finite rings were studied.…”

Section: Obviously ℛ[ ] Is An Extension Of ℛ and A Ring Embedding ℛ ⟶...mentioning

confidence: 99%

Aspects of Free Actions Based on Dependent Elements in Group Rings

Mahmood

2022

EJMS

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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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“…In recent papers [16,17,18,19,20,21,22], properties of generalized derivations, central derivations and derivations of group rings over finite rings were studied.…”

Section: Obviously ℛ[ ] Is An Extension Of ℛ and A Ring Embedding ℛ ⟶...mentioning

confidence: 99%

Aspects of Free Actions Based on Dependent Elements in Group Rings

Mahmood

2022

EJMS

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“…were studied in [8,9,28], and there is a lot of topics connected with derivations of group rings (see [33,38]). In recent papers [1,2,29], properties of generalized inner derivations, central derivations and derivations of group rings over finite rings were studied.…”

Section: History Of the Topic And Motivation For This Researchmentioning

confidence: 99%

Derivations of group rings for finite and FC groups

Arutyunov¹,

Leo²

2021

Preprint

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In this paper we establish decomposition theorems for derivations of group rings. We provide a topological technique for studying derivations of a group ring A[G] in case G has finite conjugacy classes. As a result, we describe all derivations of algebra A[G] for the case when G is a finite group, or G is an FC-group. In addition, we describe an algorithm to explicitly calculate all derivations of a group ringAs examples, derivations of Z4[S3] and F2m D2n are considered.

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