Derivations of group rings

被引：8

作者：

Artemovych, Orest D. ^{[1
]}

Bovdi, Victor A. ^{[2
]}

Salim, Mohamed A. ^{[2
]}

机构：

[1] Cracow Univ Technol, Dept Appl Math, Krakow, Poland

[2] UAEU, Al Ain, U Arab Emirates

来源：

ACTA SCIENTIARUM MATHEMATICARUM | 2020年 / 86卷 / 1-2期

关键词：

group ring; derivation; locally finite group; solder; torsion-free group; nilpotent group; differentially trivial ring; nilpotent Lie ring; solvable Lie ring; LIE IDEALS; ALGEBRAS;

D O I：

10.14232/actasm-019-664-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：51 / 72

页数：22

共 54 条

[1] ON RINGS WITH NIL COMMUTATOR IDEAL [J].

ABUKHUZAM, H .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1981, 23 (02) :307-311

[2] Derivations in differentially prime rings [J].

Al Khalaf, Ahmad ;

Artemovych, Orest D. ;

Taha, Iman .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2018, 17 (07)

[3] Rings with simple Lie rings of Lie and Jordan derivations [J].

Al Khalaf, Ahmad ;

Artemovych, Orest D. ;

Taha, Iman .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2018, 17 (04)

[4] Associative rings with metabelian adjoint group [J].

Amberg, B ;

Sysak, Y .

JOURNAL OF ALGEBRA, 2004, 277 (02) :456-473

[5]

Artemovych OD., 1998, PERIOD MATH HUNG, V36, P1, DOI DOI 10.1023/A:1004648818462

[6] Derivation rings of Lie rings [J].

Artemovych, Orest D. .

SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2019, 13 (02) :597-614

[7] AUTOMORPHISMS AND DERIVATIONS OF INCIDENCE ALGEBRAS [J].

BACLAWSKI, K .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 36 (02) :351-356

[8] Derivations on Novikov algebras [J].

Bai, CM ;

Meng, DJ ;

He, S .

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2003, 42 (03) :507-521

[9] The group of automorphisms of the Lie algebra of derivations of a polynomial algebra [J].

Bavula, V. V. .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2017, 16 (05)

[10] DERIVATIONS AND SKEW DERIVATIONS OF THE GRASSMANN ALGEBRAS [J].

Bavula, V. V. .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2009, 8 (06) :805-827

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