scholarly journals Nonlinear strong commutativity preserving maps on skew elements of prime rings with involution

2012 ◽  
Vol 436 (9) ◽  
pp. 3099-3108 ◽  
Author(s):  
Pao-Kuei Liau ◽  
Wei-Lu Huang ◽  
Cheng-Kai Liu
Keyword(s):  
Prime Rings ◽  
Rings With Involution ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity

Generalized Derivations in Rings with Involution

2017 ◽  
Vol 24 (03) ◽  
pp. 393-399 ◽  
Author(s):  
Nadeem Ahmad Dar ◽  
Abdul Nadim Khan
Keyword(s):  
Prime Ring ◽  
Related Result ◽  
Generalized Derivation ◽  
Generalized Derivations ◽  
Derivation Formula ◽  
Rings With Involution ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity

The main purpose of this paper is to study generalized derivations in rings with involution which behave like strong commutativity preserving mappings. In fact, we prove the following result: Let R be a noncommutative prime ring with involution of the second kind such that char [Formula: see text]. If R admits a generalized derivation [Formula: see text] associated with a derivation [Formula: see text] such that [Formula: see text] for all [Formula: see text], then [Formula: see text] for all [Formula: see text] or [Formula: see text] for all [Formula: see text]. Moreover, a related result is also obtained.

scholarly journals On (?,?)-Derivations and Commutativity of Prime and Semi prime ?-rings

2016 ◽  
Vol 13 (1) ◽  
pp. 198-203
Author(s):  
Baghdad Science Journal
Keyword(s):  
Prime Ring ◽  
Additive Mapping ◽  
Prime Rings ◽  
R And D ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity

Let R be a ?-ring, and ?, ? be two automorphisms of R. An additive mapping d from a ?-ring R into itself is called a (?,?)-derivation on R if d(a?b) = d(a)? ?(b) + ?(a)?d(b), holds for all a,b ?R and ???. d is called strong commutativity preserving (SCP) on R if [d(a), d(b)]? = [a,b]_?^((?,?) ) holds for all a,b?R and ???. In this paper, we investigate the commutativity of R by the strong commutativity preserving (?,?)-derivation d satisfied some properties, when R is prime and semi prime ?-ring.

On Automorphisms of Prime Rings with Involution

1997 ◽  
Vol 30 (2) ◽  
Author(s):  
L. A. Khan ◽  
A. B. Thaheem
Keyword(s):  
Prime Rings ◽  
Rings With Involution
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