Generalized Reverse Derivations on Semiprime Rings

2015 ◽  
Vol 15 ◽  
pp. 1-4
Author(s):  
C. Jaya Subba Reddy ◽  
G. Venkata Bhaskara Rao ◽  
S. Vasantha Kumar
Keyword(s):  
Prime Ring ◽  
Semiprime Rings ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity

In this paper we extend our ideas from reverse derivation towards the Generalized reverse derivations on semiprime rings. In this Paper, we prove that if d is a non-zero reverse derivation of a semi prime ring R and f is a generalized reverse derivation, thenis a strong commutativity preserving. Using this, we prove that R is commutative.

On Commutativity and Strong Commutativity-Preserving Maps

1994 ◽  
Vol 37 (4) ◽  
pp. 443-447 ◽  
Author(s):  
Howard E. Bell ◽  
Mohamad Nagy Daif
Keyword(s):  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity

AbstractIf R is a ring and S ⊆ R, a mapping f:R —> R is called strong commutativity- preserving (scp) on S if [x, y] = [f(x),f(y)] for all x,y € S. We investigate commutativity in prime and semiprime rings admitting a derivation or an endomorphism which is scp on a nonzero right ideal.

scholarly journals Strong Commutativity Preserving Maps of Semiprime Rings

1994 ◽  
Vol 37 (4) ◽  
pp. 457-460 ◽  
Author(s):  
Matej Brešar ◽  
C. Robert Miers
Keyword(s):  
Extended Centroid ◽  
Semiprime Rings ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity

AbstractIn this paper we characterize maps f: R —> R where R is semiprime, f is additive, and [f(x),f(y)] = [x,y] for all x,y ∊ R. It is shown that f(x) = λx + ξ(x) where λ ∊ C, λ2 = 1, and ξ: R —> C is additive where C is the extended centroid of R.

scholarly journals STRONG COMMUTATIVITY PRESERVING MAPPINGS ON SEMIPRIME RINGS

2006 ◽  
Vol 43 (4) ◽  
pp. 711-713 ◽  
Author(s):  
Asif Ali ◽  
Muhammad Yasen ◽  
Matloob Anwar
Keyword(s):  
Semiprime Rings ◽  
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.

scholarly journals On strong commutativity-preserving maps

2005 ◽  
Vol 2005 (6) ◽  
pp. 917-923 ◽  
Author(s):  
M. S. Samman
Keyword(s):  
Semiprime Ring ◽  
Semiprime Rings ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity ◽  
Torsion Free

We identify some strong commutativity-preserving maps on semiprime rings. Among other results, we prove the following. (i) A centralizing homomorphismfof a semiprime ringRonto itself is strong commutativity preserving. (ii) A centralizing antihomomorphismfof a 2-torsion-free semiprime ringRonto itself is strong commutativity preserving.

On Centralizing and Strong Commutativity Preserving Maps of Semiprime Rings

2015 ◽  
Vol 67 (2) ◽  
pp. 323-331
Author(s):  
Sh. Huang ◽  
Ö. Göbaşı ◽  
E. Koç
Keyword(s):  
Semiprime Rings ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity
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