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387140

On commutativity of rings with generalized derivations

Article

Last updated: 05 Jan 2025

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Abstract

Let R be a prime ring, extended centroid C , Utumi quotient ring U , and m, n ≥ 1 are
fixed positive integers, F a generalized derivation associated with a nonzero derivation d of R . We
study the case when one of the following holds: (i) F (x ) ◦m d(y ) = (x ◦ y ) n and (ii) (F (x ) ◦ d(y )) m =
(x ◦ y ) n , for all x, y in some appropriate subset of R . We also examine the case where R is a semiprime
ring.

DOI

10.1016/j.joems.2014.12.011

Keywords

Prime and semiprime rings, Generalized derivations, Martindale ring of quotients, Generalized polynomial identity (GPI), ideal

Authors

First Name

Nadeem

Last Name

ur Rehman

MiddleName

-

Affiliation

Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Email

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City

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Orcid

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First Name

Mohd

Last Name

Raza

MiddleName

Arif

Affiliation

Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Email

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City

-

Orcid

-

First Name

Tarannum

Last Name

Bano

MiddleName

-

Affiliation

Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Email

-

City

-

Orcid

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Volume

24

Article Issue

2

Related Issue

51062

Issue Date

2016-06-01

Receive Date

2024-10-20

Publish Date

2016-06-01

Page Start

151

Page End

155

Print ISSN

1110-256X

Online ISSN

2090-9128

Article File

JOEMS_Volume 24_Issue 2_Pages 151-155.pdf

PDF . 349.7kB

Link

https://joems.journals.ekb.eg/article_387140.html

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https://joems.journals.ekb.eg/service?article_code=387140

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387,140

Publication Type

Journal

Publication Title

Journal of the Egyptian Mathematical Society

Publication Link

https://joems.journals.ekb.eg/

MainTitle

On commutativity of rings with generalized derivations

Details

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Article

Created At

21 Dec 2024