On certain classes of generalized derivations

2019 ◽  
Vol 69 (5) ◽  
pp. 1023-1032 ◽  
Author(s):  
Omar Ait Zemzami ◽  
Lahcen Oukhtite ◽  
Shakir Ali ◽  
Najat Muthana
Keyword(s):  
Generalized Derivations ◽  
Prime Rings ◽  
Rings With Involution

Abstract Our purpose in this paper is to investigate some particular classes of generalized derivations and their relationship with commutativity of prime rings with involution. Some well-known results characterizing commutativity of prime rings have been generalized. Furthermore, we provide examples to show that the assumed restrictions cannot be relaxed.

scholarly journals A characterization of $ b- $generalized derivations on prime rings with involution

2021 ◽  
Vol 7 (2) ◽  
pp. 2413-2426
Author(s):  
Mohd Arif Raza ◽  
◽  
Abdul Nadim Khan ◽  
Husain Alhazmi ◽  
Keyword(s):  
Generalized Derivations ◽  
Prime Rings ◽  
Functional Identities ◽  
Rings With Involution

<abstract><p>In this note, we characterize $ b- $generalized derivations which are strong commutative preserving (SCP) on $ \mathscr{R} $. Moreover, we also discuss and characterize $ b- $generalized derivations involving certain $ \ast- $differential/functional identities on rings possessing involution.</p></abstract>

Differential identities on prime rings with involution

2018 ◽  
Vol 17 (09) ◽  
pp. 1850163 ◽  
Author(s):  
A. Mamouni ◽  
B. Nejjar ◽  
L. Oukhtite
Keyword(s):  
Generalized Derivations ◽  
Prime Rings ◽  
Differential Identities ◽  
Rings With Involution

In this paper, we investigate commutativity of prime rings [Formula: see text] with involution ∗ of the second kind in which generalized derivations satisfy certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been generalized. Furthermore, we provide an example to show that the restriction imposed on the involution is not superfluous.

A study of differential prime rings with involution

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Lahcen Oukhtite ◽  
Omar Ait Zemzami
Keyword(s):  
Generalized Derivations ◽  
Prime Rings ◽  
Rings With Involution

Abstract The main goal of the present paper is to study some results concerning generalized derivations of prime rings with involution. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.

Some commutativity theorems for rings with involution involving generalized derivations

2019 ◽  
Vol 12 (01) ◽  
pp. 1950001 ◽  
Author(s):  
My Abdallah Idrissi ◽  
Lahcen Oukhtite
Keyword(s):  
Generalized Derivation ◽  
Generalized Derivations ◽  
Prime Rings ◽  
Commutativity Theorems ◽  
Rings With Involution

Our purpose in this paper is to investigate commutativity of a ring with involution [Formula: see text] which admits a generalized derivation satisfying certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been generalized. Moreover, we provide examples to show that the assumed restrictions cannot be relaxed.

scholarly journals On Maps of Period 2 on Prime and Semiprime Rings

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
H. E. Bell ◽  
M. N. Daif
Keyword(s):  
Generalized Derivations ◽  
Prime Rings ◽  
Period 2 ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Rings With Involution

A mapfof the ringRinto itself is of period 2 iff2x=xfor allx∈R; involutions are much studied examples. We present some commutativity results for semiprime and prime rings with involution, and we study the existence of derivations and generalized derivations of period 2 on prime and semiprime rings.

scholarly journals A classification of generalized derivations in rings with involution

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1439-1452
Author(s):  
Bharat Bhushan ◽  
Gurninder Sandhu ◽  
Shakir Ali ◽  
Deepak Kumar
Keyword(s):  
Generalized Derivation ◽  
Additive Mapping ◽  
Generalized Derivations ◽  
Prime Rings ◽  
Rings With Involution

Let R be a ring. An additive mapping F : R ? R is called a generalized derivation if there exists a derivation d of R such that F(xy) = F(x)y + xd(y) for all x,y ? R. The main purpose of this paper is to characterize some specific classes of generalized derivations of rings. Precisely, we describe the structure of generalized derivations of noncommutative prime rings with involution that belong to a particular class of generalized derivations. Consequently, some recent results in this line of investigation have been extended. Moreover, some suitable examples showing that the assumed hypotheses are crucial, are also given.

Generalized derivations on prime rings with involution

2018 ◽  
pp. 317-332
Author(s):  
Omar Ait Zemzami ◽  
Abdellah Mamouni ◽  
Lahcen Oukhtite
Keyword(s):  
Generalized Derivations ◽  
Prime Rings ◽  
Rings With Involution
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