scholarly journals Left Multiplicative Generalized Jordan Derivations of Semiprime Rings

2018 ◽  
Vol 12 (1) ◽  
Author(s):  
Reddy CJS ◽  
Nagesh K ◽  
Kumar AS
Keyword(s):  
Semiprime Rings

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.

Derivations of differentially semiprime rings

2019 ◽  
Vol 12 (05) ◽  
pp. 1950079
Author(s):  
Ahmad Al Khalaf ◽  
Iman Taha ◽  
Orest D. Artemovych ◽  
Abdullah Aljouiiee
Keyword(s):  
Commutative Ring ◽  
Semiprime Ring ◽  
Prime Rings ◽  
Commutative Case ◽  
Lie Ring ◽  
Lie Rings ◽  
Semiprime Rings ◽  
Torsion Free

Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der [Formula: see text] of derivations in a commutative differentially prime rings [Formula: see text]. We study Lie rings Der [Formula: see text] in the non-commutative case and prove that if [Formula: see text] is a [Formula: see text]-torsion-free [Formula: see text]-semiprime ring, then [Formula: see text] is a semiprime Lie ring or [Formula: see text] is a commutative ring.

scholarly journals Some results concerning n-σ-centralizing mappings in semiprime rings

2014 ◽  
Vol 3 (1) ◽  
pp. 15-21
Author(s):  
Vincenzo De Filippis ◽  
Basudeb Dhara
Keyword(s):  
Semiprime Rings

Annihilator condition of a pair of derivations in prime and semiprime rings

2016 ◽  
Vol 47 (1) ◽  
pp. 111-124 ◽  
Author(s):  
Basudeb Dhara ◽  
Nurcan Argaç ◽  
Krishna Gopal Pradhan
Keyword(s):  
Prime And Semiprime Rings ◽  
Semiprime Rings

scholarly journals Identities with derivations and automorphisms on semiprime rings

2005 ◽  
Vol 2005 (7) ◽  
pp. 1031-1038 ◽  
Author(s):  
Joso Vukman
Keyword(s):  
Prime Ring ◽  
Classical Result ◽  
Semiprime Rings

The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. Mayne proved that in case there exists a nontrivial centralizing automorphism on a prime ring, then the ring is commutative. In this paper, some results related to Posner's theorem as well as to Mayne's theorem are proved.

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