scholarly journals Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings

2016 ◽  
Vol 66 (1) ◽  
pp. 271-292
Author(s):  
Vincenzo De Filippis
Keyword(s):  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity

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 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.

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

A Note on Differential Identities in Prime and Semiprime Rings

2020 ◽  
pp. 77-83
Author(s):  
Mohammad Shadab Khan ◽  
Mohd Arif Raza ◽  
Nadeemur Rehman
Keyword(s):  
Prime Ring ◽  
Semiprime Ring ◽  
Nonzero Ideal ◽  
Differential Identities ◽  
Standard Identity ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Positive Integers

Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and m, n fixed positive integers. (i) If (d ( r ○ s)(r ○ s) + ( r ○ s) d ( r ○ s)n - d ( r ○ s))m for all r, s ϵ I, then R is commutative. (ii) If (d ( r ○ s)( r ○ s) + ( r ○ s) d ( r ○ s)n - d (r ○ s))m ϵ Z(R) for all r, s ϵ I, then R satisfies s4, the standard identity in four variables. Moreover, we also examine the case when R is a semiprime ring.

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