Derivations of group rings

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

doi:10.14232/ACTASM-019-664-X

Derivations of group rings

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

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Let R[G] be the group ring of a group G over an associative ring R with unity such that all prime divisors of orders of elements of G are invertible in R. If R is finite and G is a Chernikov (torsion FC-) group, then each R-derivation of R[G] is inner. Similar results also are obtained for other classes of groups G and rings R.

Original language	English
Pages (from-to)	51-72
Number of pages	22
Journal	Acta Scientiarum Mathematicarum
Volume	86
Issue number	1-2
DOIs	https://doi.org/10.14232/ACTASM-019-664-X
Publication status	Published - 2020
Externally published	Yes

Keywords

Derivation
Differentially trivial ring
Group ring
Locally finite group
Nilpotent group
Nilpotent lie ring
Solder
Solvable lie ring
Torsion-free group

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.14232/ACTASM-019-664-X

Cite this

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title = "Derivations of group rings",

abstract = "Let R[G] be the group ring of a group G over an associative ring R with unity such that all prime divisors of orders of elements of G are invertible in R. If R is finite and G is a Chernikov (torsion FC-) group, then each R-derivation of R[G] is inner. Similar results also are obtained for other classes of groups G and rings R.",

keywords = "Derivation, Differentially trivial ring, Group ring, Locally finite group, Nilpotent group, Nilpotent lie ring, Solder, Solvable lie ring, Torsion-free group",

author = "Artemovych, \{Orest D.\} and Bovdi, \{Victor A.\} and Salim, \{Mohamed A.\}",

note = "Publisher Copyright: {\textcopyright} Bolyai Institute, University of Szeged.",

year = "2020",

doi = "10.14232/ACTASM-019-664-X",

language = "English",

volume = "86",

pages = "51--72",

journal = "Acta Scientiarum Mathematicarum",

issn = "0001-6969",

publisher = "Springer International Publishing",

number = "1-2",

}

TY - JOUR

T1 - Derivations of group rings

AU - Artemovych, Orest D.

AU - Bovdi, Victor A.

AU - Salim, Mohamed A.

N1 - Publisher Copyright: © Bolyai Institute, University of Szeged.

PY - 2020

Y1 - 2020

N2 - Let R[G] be the group ring of a group G over an associative ring R with unity such that all prime divisors of orders of elements of G are invertible in R. If R is finite and G is a Chernikov (torsion FC-) group, then each R-derivation of R[G] is inner. Similar results also are obtained for other classes of groups G and rings R.

AB - Let R[G] be the group ring of a group G over an associative ring R with unity such that all prime divisors of orders of elements of G are invertible in R. If R is finite and G is a Chernikov (torsion FC-) group, then each R-derivation of R[G] is inner. Similar results also are obtained for other classes of groups G and rings R.

KW - Derivation

KW - Differentially trivial ring

KW - Group ring

KW - Locally finite group

KW - Nilpotent group

KW - Nilpotent lie ring

KW - Solder

KW - Solvable lie ring

KW - Torsion-free group

UR - https://www.scopus.com/pages/publications/85089900021

UR - https://www.scopus.com/pages/publications/85089900021#tab=citedBy

U2 - 10.14232/ACTASM-019-664-X

DO - 10.14232/ACTASM-019-664-X

M3 - Article

AN - SCOPUS:85089900021

SN - 0001-6969

VL - 86

SP - 51

EP - 72

JO - Acta Scientiarum Mathematicarum

JF - Acta Scientiarum Mathematicarum

IS - 1-2

ER -

Derivations of group rings

Abstract

Keywords

ASJC Scopus subject areas

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