scholarly journals Generalized Strong Commutativity Preserving Centralizers of Semiprime Γ- Rings

2019 ◽  
pp. 2223-2228
Author(s):  
Shahed Ali Hamil ◽  
Abdulrahman H. Majeed
Keyword(s):  
Strong Commutativity Preserving ◽  
Strong Commutativity ◽  
Classical Ring

     In this paper, we introduce the concept of generalized strong commutativity (Cocommutativity) preserving right centralizers on a subset of a Γ-ring. And we generalize some results of a classical ring to a gamma ring.

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 skew derivations on Banach algebras

2019 ◽  
Vol 13 (1) ◽  
pp. 478-480
Author(s):  
Abdul Nadim Khan ◽  
Mohd Arif Raza ◽  
Husain Alhazmi
Keyword(s):  
Banach Algebras ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity

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.

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