On Jordan and Jordan*-generalized derivations in semiprime rings with involution

2007 ◽  
Vol 2 ◽  
pp. 1487-1492 ◽  
Author(s):  
M. N. Daif ◽  
M. S. Tammam El-Sayiad
Keyword(s):  
Generalized Derivations ◽  
Semiprime Rings ◽  
Rings With Involution

scholarly journals On Maps of Period 2 on Prime and Semiprime Rings

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
H. E. Bell ◽  
M. N. Daif
Keyword(s):  
Generalized Derivations ◽  
Prime Rings ◽  
Period 2 ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Rings With Involution

A mapfof the ringRinto itself is of period 2 iff2x=xfor allx∈R; involutions are much studied examples. We present some commutativity results for semiprime and prime rings with involution, and we study the existence of derivations and generalized derivations of period 2 on prime and semiprime rings.

On generalized derivations of semiprime rings with involution

2007 ◽  
Vol 1 ◽  
pp. 551-555 ◽  
Author(s):  
M. N. Daif ◽  
M. S. Tammam El-Sayiad
Keyword(s):  
Generalized Derivations ◽  
Semiprime Rings ◽  
Rings With Involution

Identities with Generalized Derivations and Automorphisms on Semiprime Rings

2015 ◽  
Vol 2 (1) ◽  
pp. 24-29
Author(s):  
Asma Ali ◽  
◽  
Shahoor Khan ◽  
Khalid Hamdin
Keyword(s):  
Generalized Derivations ◽  
Semiprime Rings

scholarly journals Generalized Derivations on Power Values of Lie Ideals in Prime and Semiprime Rings

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Vincenzo De Filippis ◽  
Nadeem UR Rehman ◽  
Abu Zaid Ansari
Keyword(s):  
Lie Ideal ◽  
Generalized Derivations ◽  
Fixed Integer ◽  
Free Ring ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Positive Integers ◽  
Torsion Free

LetRbe a 2-torsion free ring and letLbe a noncentral Lie ideal ofR, and letF:R→RandG:R→Rbe two generalized derivations ofR. We will analyse the structure ofRin the following cases: (a)Ris prime andF(um)=G(un)for allu∈Land fixed positive integersm≠n; (b)Ris prime andF((upvq)m)=G((vrus)n)for allu,v∈Land fixed integersm,n,p,q,r,s≥1; (c)Ris semiprime andF((uv)n)=G((vu)n)for allu,v∈[R,R]and fixed integern≥1; and (d)Ris semiprime andF((uv)n)=G((vu)n)for allu,v∈Rand fixed integern≥1.

Semiprime rings with multiplicative (generalized)- derivations involving left multipliers

2021 ◽  
Vol 30 (1) ◽  
pp. 61-68
Author(s):  
G. NAGA MALLESWARI ◽  
S. SREENIVASULU ◽  
G. SHOBHALATHA
Keyword(s):  
Generalized Derivations ◽  
Semiprime Rings

On generalized derivations in semiprime rings involving anticommutator

2019 ◽  
Vol 60 (3) ◽  
pp. 587-598
Author(s):  
Mohammad Ashraf ◽  
Sajad Ahmad Pary ◽  
Mohd Arif Raza
Keyword(s):  
Generalized Derivations ◽  
Semiprime Rings

scholarly journals Some identities involving multiplicative generalized derivations in orime and semiprime rings

2018 ◽  
Vol 36 (1) ◽  
pp. 25 ◽  
Author(s):  
Basudeb Dhara
Keyword(s):  
Generalized Derivation ◽  
Generalized Derivations ◽  
Semiprime Rings

Let $R$ be a ring with center $Z(R)$. A mapping $F:R\rightarrow R$ is called a multiplicative generalized derivation, if $F(xy)=F(x)y+xg(y)$ is fulfilled for all $x,y\in R$, where $g:R\rightarrow R$ is a derivation. In the present paper, our main object is to study the situations: (1) $F(xy)- F(x)F(y)\in Z(R)$, (2) $F(xy)+ F(x)F(y)\in Z(R)$, (3) $F(xy)- F(y)F(x)\in Z(R)$, (4) $F(xy)+ F(y)F(x)\in Z(R)$, (5) $F(xy)- g(y)F(x)\in Z(R)$; for all $x,y$ in some suitable subset of $R$.

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