JORDAN REGULAR UNITS IN RINGS AND GROUP RINGS

被引：0

作者：

Kumari, P. ^{[1
]}

Sahai, M. ^{[2
]}

Sharma, R. K. ^{[3
]}

机构：

[1] Govt PG Coll Women, Rohtak, Haryana, India

[2] Lucknow Univ, Dept Math & Astron, Lucknow, Uttar Pradesh, India

[3] Indian Inst Technol Delhi, Dept Math, New Delhi, India

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2023年 / 75卷 / 3期

关键词：

D O I：

10.1007/s11253-023-02207-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The concept of Lie regular elements and Lie regular units was defined and studied by Kanwar, Sharma, and Yadav in Comm. Algebra, 40, No. 4, 1304-1315 (2012). We introduce Jordan regular elements and Jordan regular units. It is proved that the order of the set of Jordan regular units in M(2, Z(2n)) is equal to a half of the order of U(M(2, Z(2n))). Further, we show that the group ring KG of a group G over a field K of characteristic 2 has no Jordan regular units.

引用

页码：403 / 418

页数：16

共 50 条

[1] Jordan Regular Units in Rings and Group Rings
P. Kumari
M. Sahai
R. K. Sharma
Ukrainian Mathematical Journal, 2023, 75 : 403 - 418
[2] UNITS IN REGULAR ABELIAN P-GROUP RINGS
HOECHSMANN, K
SEHGAL, SK
JOURNAL OF NUMBER THEORY, 1988, 30 (03) : 375 - 381
[3] UNITS IN REGULAR ELEMENTARY ABELIAN GROUP-RINGS
HOECHSMANN, K
SEHGAL, SK
ARCHIV DER MATHEMATIK, 1986, 47 (05) : 413 - 417
[4] JORDAN DECOMPOSITION AND HYPERCENTRAL UNITS IN INTEGRAL GROUP-RINGS
ARORA, SR
HALES, AW
PASSI, IBS
COMMUNICATIONS IN ALGEBRA, 1993, 21 (01) : 25 - 35
[5] UNITS OF GROUP RINGS
DENNIS, RK
JOURNAL OF ALGEBRA, 1976, 43 (02) : 655 - 664
[6] UNITS OF GROUP RINGS
DENNIS, RK
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 23 (06): : A606 - A606
[7] Units of group rings
Jespers, E
Milies, CP
JOURNAL OF PURE AND APPLIED ALGEBRA, 1996, 107 (2-3) : 233 - 251
[8] The units of group rings
Higman, G
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1940, 46 : 231 - 248
[9] Group rings and Jordan decomposition
Hales, Alfred W.
Passi, Inder Bir S.
GROUPS, RINGS, GROUP RINGS, AND HOPF ALGEBRAS, 2017, 688 : 103 - 111
[10] Jordan nilpotency in group rings
Goodaire, Edgar G.
Milies, Cesar Polcino
JOURNAL OF GROUP THEORY, 2014, 17 (04) : 541 - 557

← 1 2 3 4 5 →