Derivation rings of Lie rings

Artemovych, Orest D.

doi:10.1007/s40863-017-0077-5

Cited by 8 publications

(6 citation statements)

References 28 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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“…In as much as A is abelian and bd ∈ A, Eqs. (6) imply that δ(b)d = 0. This yields that (δ(B)B) 2 = 0.…”

Section: Locally Inner Derivationsmentioning

confidence: 99%

“…)-bimodule of all functions from G in K). Derivations of certain rings were investigated in [2,3,6,7,8,9,10,31,32,33,34,35,36,37,42,45,48].…”

Section: Introductionmentioning

confidence: 99%

Derivations of group rings

Artemovych,

Bovdi,

Salim

2020

Preprint

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Derivation rings of Lie rings

Abstract: We establish some connections between Lie rings, their derivation rings and generalized derivations rings.

Cited by 8 publications

References 28 publications

Aspects of Free Actions Based on Dependent Elements in Group Rings

Aspects of Free Actions Based on Dependent Elements in Group Rings

Derivations of group rings for finite and FC groups

Derivations of group rings

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