Some results on ideals of semiprime rings with multiplicative generalized derivations

被引：10

作者：

Koc, Emine ^{[1
]}

Golbasi, Oznur ^{[1
]}

机构：

[1] Cumhuriyet Univ, Dept Math, Fac Sci, Sivas, Turkey

来源：

COMMUNICATIONS IN ALGEBRA | 2018年 / 46卷 / 11期

关键词：

Centralizing mapping; commuting mapping; ideal; multiplicative generalized derivation; SCP map; semiprime ring; COMMUTATIVITY; MAPPINGS; PRIME;

D O I：

10.1080/00927872.2018.1459644

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a semiprime ring and I a nonzero ideal of R. A map F:RR is called a multiplicative generalized derivation if there exists a map d:RR such that F(xy)=F(x)y+xd(y), for all x,yR. In the present paper, we shall prove that R contains a nonzero central ideal if any one of the following holds: i) iii) F is SCP on I, iv) F(u)degrees F(v)=u degrees v, for all u,v is an element of I.

引用

页码：4905 / 4913

页数：9

共 50 条

[1] MULTIPLICATIVE GENERALIZED DERIVATIONS ON IDEALS IN SEMIPRIME RINGS
Golbas, Oznur
[J]. MATHEMATICA SLOVACA, 2016, 66 (06) : 1285 - 1296
[2] Multiplicative (generalized)-derivations and left ideals in semiprime rings
Ali, Asma
Dhara, Basudeb
Khan, Shahoor
Ali, Farhat
[J]. HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2015, 44 (06): : 1293 - 1306
[3] On Lie ideals with multiplicative (generalized)-derivations in prime and semiprime rings
Ali S.
Dhara B.
Dar N.A.
Khan A.N.
[J]. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2015, 56 (1): : 325 - 337
[4] A note on multiplicative (generalized)-derivations and left ideals in semiprime rings
Basudeb Dhara
Sukhendu Kar
Swarup Kuila
[J]. Rendiconti del Circolo Matematico di Palermo Series 2, 2021, 70 : 631 - 640
[5] NOTES ON LEFT IDEALS OF SEMIPRIME RINGS WITH MULTIPLICATIVE GENERALIZED (α, α) - DERIVATIONS
Ulutas, Ercan
Golbasi, Oznur
[J]. FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2021, 36 (04): : 903 - 912
[6] MULTIPLICATIVE GENERALIZED DERIVATIONS ON LIE IDEALS IN SEMIPRIME RINGS II
Koc, Emine
Golbasi, Oznur
[J]. MISKOLC MATHEMATICAL NOTES, 2017, 18 (01) : 265 - 276
[7] A note on multiplicative (generalized)-derivations and left ideals in semiprime rings
Dhara, Basudeb
Kar, Sukhendu
Kuila, Swarup
[J]. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2021, 70 (02) : 631 - 640
[8] On semiprime rings with multiplicative (generalized)-derivations
Khan S.
[J]. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2016, 57 (1): : 119 - 128
[9] IDENTITIES WITH MULTIPLICATIVE GENERALIZED ( α, α )-DERIVATIONS OF SEMIPRIME RINGS
Sandhu, Gurninder Singh
Ayran, Ayse
Aydin, Neset
[J]. KRAGUJEVAC JOURNAL OF MATHEMATICS, 2024, 48 (03): : 365 - 382
[10] On multiplicative (generalized)-derivations in prime and semiprime rings
Dhara, Basudeb
Ali, Shakir
[J]. AEQUATIONES MATHEMATICAE, 2013, 86 (1-2) : 65 - 79

← 1 2 3 4 5 →