scholarly journals Generalized derivations acting as homomorphism or anti-homomorphism with central values in semiprime rings

2015 ◽  
Vol 16 (2) ◽  
pp. 781-791 ◽  
Author(s):  
Basudeb Dhara ◽  
Sukhendu Kar ◽  
Krishna Gopal Pradahan
Keyword(s):  
Generalized Derivations ◽  
Central Values ◽  
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

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 $R$.

scholarly journals On Generalized ()-Derivations in Semiprime Rings

ISRN Algebra ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Basudeb Dhara ◽  
Atanu Pattanayak
Keyword(s):  
Semiprime Ring ◽  
Generalized Derivation ◽  
Additive Mapping ◽  
Nonzero Ideal ◽  
Generalized Derivations ◽  
Semiprime Rings

Let be a semiprime ring, a nonzero ideal of , and , two epimorphisms of . An additive mapping is generalized -derivation on if there exists a -derivation such that holds for all . In this paper, it is shown that if , then contains a nonzero central ideal of , if one of the following holds: (i) ; (ii) ; (iii) ; (iv) ; (v) for all .

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