scholarly journals Jordan Derivations on Lie Ideals of ?-Prime Rings

2017 ◽  
Vol 36 ◽  
pp. 1-5
Author(s):  
Akhil Chandra Paul ◽  
Md Mizanor Rahman
Keyword(s):  
Prime Ring ◽  
Additive Mapping ◽  
Lie Ideal ◽  
Prime Rings ◽  
R And D ◽  
Square Closed Lie Ideal ◽  
Torsion Free

In this paper we prove that, if U is a s-square closed Lie ideal of a 2-torsion free s-prime ring R and  d: R(R is an additive mapping satisfying d(u2)=d(u)u+ud(u) for all u?U then d(uv)=d(u)v+ud(v) holds for all  u,v?UGANIT J. Bangladesh Math. Soc.Vol. 36 (2016) 1-5

scholarly journals Derivations on Lie Ideals of σ-Prime Γ-Rings

2015 ◽  
Vol 39 (2) ◽  
pp. 249-255
Author(s):  
Md Mizanor Rahman ◽  
Akhil Chandra Paul
Keyword(s):  
Prime Ring ◽  
Additive Mapping ◽  
Jordan Derivation ◽  
Lie Ideal ◽  
Square Closed Lie Ideal ◽  
Academy Of Sciences ◽  
Gamma Rings ◽  
Torsion Free

The authors extend and generalize some results of previous workers to ?-prime ?-ring. For a ?-square closed Lie ideal U of a 2-torsion free ?-prime ?-ring M, let d: M ?M be an additive mapping satisfying d(u?u)=d(u)? u + u?d(u) for all u ? U and ? ? ?. The present authors proved that d(u?v) = d(u)?v + u?d(v) for all u, v ? U and ?? ?, and consequently, every Jordan derivation of a 2-torsion free ?-prime ?-ring M is a derivation of M.Journal of Bangladesh Academy of Sciences, Vol. 39, No. 2, 249-255, 2015

Generalized derivations on Lie ideals in prime rings

2016 ◽  
Vol 10 (02) ◽  
pp. 1750032 ◽  
Author(s):  
V. K. Yadav ◽  
S. K. Tiwari ◽  
R. K. Sharma
Keyword(s):  
Prime Ring ◽  
Lie Ideal ◽  
Generalized Derivations ◽  
Prime Rings ◽  
Square Closed Lie Ideal ◽  
Torsion Free

Let [Formula: see text] be a [Formula: see text]-torsion free prime ring, and [Formula: see text] a square closed Lie ideal of [Formula: see text] Further let [Formula: see text] and [Formula: see text] be generalized derivations associated with derivations [Formula: see text] and [Formula: see text], respectively on [Formula: see text] If one of the following conditions holds: (i) [Formula: see text] (ii) [Formula: see text] (iii) [Formula: see text] (iv) [Formula: see text] (v) [Formula: see text] for all [Formula: see text] then it is proved that either [Formula: see text] or [Formula: see text]

scholarly journals Generalized Derivations Acting as Homomorphisms and Anti-Homomorphisms on Lie Ideals of Prime Rings

2016 ◽  
Vol 35 ◽  
pp. 73-77
Author(s):  
Akhil Chandra Paul ◽  
Sujoy Chakraborty
Keyword(s):  
Prime Ring ◽  
Generalized Derivation ◽  
Lie Ideal ◽  
Generalized Derivations ◽  
Prime Rings ◽  
Square Closed Lie Ideal ◽  
Torsion Free

Let U be a non-zero square closed Lie ideal of a 2-torsion free prime ring R and f a generalized derivation of R with the associated derivation d of R. If f acts as a homomorphism and as an anti-homomorphism on U, then we prove that d = 0 or U € Z(R), the centre of R.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 73-77

scholarly journals Semiderivations Satisfying Certain Algebraic Identities on Jordan Ideals

ISRN Algebra ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Vincenzo De Filippis ◽  
Abdellah Mamouni ◽  
Lahcen Oukhtite
Keyword(s):  
Prime Ring ◽  
Additive Mapping ◽  
Prime Rings ◽  
Torsion Free

Let be a ring. An additive mapping is called semiderivation of if there exists an endomorphism of such that and , for all in . Here we prove that if is a 2-torsion free -prime ring and a nonzero -Jordan ideal of such that for all , then either is commutative or for all . Moreover, we initiate the study of generalized semiderivations in prime rings.

scholarly journals (U, M) -derivations in prime ?-rings

2016 ◽  
Vol 27 (2) ◽  
pp. 143-153
Author(s):  
MM Rahman ◽  
AC Paul
Keyword(s):  
Prime Ring ◽  
Lie Ideal ◽  
Prime Rings ◽  
Torsion Free

In this article, we define (U,M)-derivation d of a ? -ring M . For a Lie ideal U of a 2 - torsion free prime ? -ring M satisfying the condition a?b?c = a?b?c for all a,b, c?M and ? ,? ?? , we prove the following results:(i) ifU is an admissible Lie ideal of M, then d(u?v) = d(u)?v + u?d(v) for all u, v?U ,? ??(ii) if u?u?U for all u?U,? ?? , then d(u?m) = d(u)?m + u?d(m) for all m ? M Bangladesh J. Sci. Res. 27(2): 143-153, December-2014

scholarly journals On Jordan ideals and left(θ,θ)-derivations in prime rings

2004 ◽  
Vol 2004 (37) ◽  
pp. 1957-1964 ◽  
Author(s):  
S. M. A. Zaidi ◽  
Mohammad Ashraf ◽  
Shakir Ali
Keyword(s):  
Prime Ring ◽  
Nonempty Subset ◽  
Additive Mapping ◽  
Prime Rings ◽  
Torsion Free

LetRbe a ring andSa nonempty subset ofR. Suppose thatθandϕare endomorphisms ofR. An additive mappingδ:R→Ris called a left(θ,ϕ)-derivation (resp., Jordan left(θ,ϕ)-derivation) onSifδ(xy)=θ(x)δ(y)+ϕ(y)δ(x)(resp.,δ(x2)=θ(x)δ(x)+ϕ(x)δ(x)) holds for allx,y∈S. Suppose thatJis a Jordan ideal and a subring of a2-torsion-free prime ringR. In the present paper, it is shown that ifθis an automorphism ofRsuch thatδ(x2)=2θ(x)δ(x)holds for allx∈J, then eitherJ⫅Z(R)orδ(J)=(0). Further, a study of left(θ,θ)-derivations of a prime ringRhas been made which acts either as a homomorphism or as an antihomomorphism of the ringR.

Generalized Jordan Semiderivations in Prime Rings

2015 ◽  
Vol 58 (2) ◽  
pp. 263-270 ◽  
Author(s):  
Vincenzo De Filippis ◽  
Abdellah Mamouni ◽  
Lahcen Oukhtite
Keyword(s):  
Prime Ring ◽  
Additive Mapping ◽  
Prime Rings ◽  
R And D

AbstractLet R be a ring and let g be an endomorphism of R. The additive mapping d: R → R is called a Jordan semiderivation of R, associated with g, ifd(x2) = d(x)x + g(x)d(x) = d(x)g(x) + xd(x) and d(g(x)) = g(d(x))for all x ∊ R. The additive mapping F: R → R is called a generalized Jordan semiderivation of R, related to the Jordan semiderivation d and endomorphism g, ifF(x2) = F(x)x + g(x)d(x) = F(x)g(x) + xd(x) and F(g(x)) = g(F(x))for all x ∊ R. In this paper we prove that if R is a prime ring of characteristic different from 2, g an endomorphism of R, d a Jordan semiderivation associated with g, F a generalized Jordan semiderivation associated with d and g, then F is a generalized semiderivation of R and d is a semiderivation of R. Moreover, if R is commutative, then F = d.

scholarly journals On (?,?)-Derivations and Commutativity of Prime and Semi prime ?-rings

2016 ◽  
Vol 13 (1) ◽  
pp. 198-203
Author(s):  
Baghdad Science Journal
Keyword(s):  
Prime Ring ◽  
Additive Mapping ◽  
Prime Rings ◽  
R And D ◽  
Strong Commutativity Preserving ◽  
Strong Commutativity

Let R be a ?-ring, and ?, ? be two automorphisms of R. An additive mapping d from a ?-ring R into itself is called a (?,?)-derivation on R if d(a?b) = d(a)? ?(b) + ?(a)?d(b), holds for all a,b ?R and ???. d is called strong commutativity preserving (SCP) on R if [d(a), d(b)]? = [a,b]_?^((?,?) ) holds for all a,b?R and ???. In this paper, we investigate the commutativity of R by the strong commutativity preserving (?,?)-derivation d satisfied some properties, when R is prime and semi prime ?-ring.

Permuting tri-derivations in prime and semi-prime rings

2016 ◽  
Vol 5 (1) ◽  
pp. 52
Author(s):  
H. Durna ◽  
S. OĞUZ
Keyword(s):  
Prime Ring ◽  
Lie Ideal ◽  
Prime Rings ◽  
Square Closed Lie Ideal

Let \(R\) be a ring and \(U\neq0\) be a square closed Lie ideal of \(R\). A tri-additive permuting map \(D:R\times R\times R\rightarrow R\) is called permuting tri-derivation if, for any \(y,z\in R\), the map \(x\mapsto D(x,y,z)\) is a derivation. A mapping \(d:R\rightarrow R\) defined by \(d(x)=D(x,x,x)\) is called the trace of \(D\). In the present paper, we show that \(U\subseteq Z\) such that \(R\) is a prime and semi-prime ring admitting the trace $d$ satisfying the several conditions of permuting tri-derivation.

scholarly journals On Higher N-Derivation Of Prime Rings

2014 ◽  
Vol 11 (2) ◽  
pp. 211-219
Author(s):  
Baghdad Science Journal
Keyword(s):  
Prime Ring ◽  
Prime Rings ◽  
Torsion Free

The main purpose of this work is to introduce the concept of higher N-derivation and study this concept into 2-torsion free prime ring we proved that:Let R be a prime ring of char. 2, U be a Jordan ideal of R and be a higher N-derivation of R, then , for all u U , r R , n N .

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