scholarly journals Generalized derivations with left annihilator conditions in prime and semiprime rings

2017 ◽  
Vol 37 (2) ◽  
pp. 161 ◽  
Author(s):  
Basudeb Dhara
Keyword(s):  
Generalized Derivations ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Left Annihilator

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.

Generalized derivations preserving Engel condition in prime and semiprime rings

2020 ◽  
pp. 2150041
Author(s):  
Rita Prestigiacomo
Keyword(s):  
Prime Ring ◽  
Algebraic Closure ◽  
Quotient Ring ◽  
Lie Ideal ◽  
Extended Centroid ◽  
Generalized Derivations ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Martindale Quotient Ring ◽  
Engel Condition

Let [Formula: see text] be a prime ring with [Formula: see text], [Formula: see text] a non-central Lie ideal of [Formula: see text], [Formula: see text] its Martindale quotient ring and [Formula: see text] its extended centroid. Let [Formula: see text] and [Formula: see text] be nonzero generalized derivations on [Formula: see text] such that [Formula: see text] Then there exists [Formula: see text] such that [Formula: see text] and [Formula: see text], for any [Formula: see text], unless [Formula: see text], where [Formula: see text] is the algebraic closure of [Formula: see text].

scholarly journals On Orthogonal Generalized Derivations of Semiprime -Rings

2019 ◽  
Vol 39 ◽  
pp. 63-70
Author(s):  
Kalyan Kumar Dey ◽  
Sanjay Kumar Saha ◽  
Akhil Chandra Paul
Keyword(s):  
Generalized Derivations ◽  
Semiprime Rings ◽  
Left Annihilator

In this paper, we study the orthogonality of two generalized derivations in semiprime G-rings. Some results are obtained in connection with ideals of semiprime G-rings and using left annihilator which is taken to be zero. GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 63-70

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.

scholarly journals Generalized Derivations and Left Ideals in Prime and Semiprime Rings

ISRN Algebra ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-5 ◽  
Author(s):  
Basudeb Dhara ◽  
Atanu Pattanayak
Keyword(s):  
Left Ideal ◽  
Associative Ring ◽  
Generalized Derivation ◽  
Generalized Derivations ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings

Let R be an associative ring, λ a nonzero left ideal of R, d:R→R a derivation and G:R→R a generalized derivation. In this paper, we study the following situations in prime and semiprime rings: (1) G(x∘y)=a(xy±yx); (2) G[x,y]=a(xy±yx); (3) d(x)∘d(y)=a(xy±yx); for all x,y∈λ and a∈{0,1,-1}.

scholarly journals Generalized (; )-derivations and Left Ideals in Prime and Semiprime Rings

2017 ◽  
Vol 13 (2) ◽  
pp. 7163-7167
Author(s):  
Asma Ali ◽  
Hamidur Rahaman
Keyword(s):  
Left Ideal ◽  
Associative Ring ◽  
Generalized Derivation ◽  
Generalized Derivations ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings

Let R be an associative ring, ; be the automorphisms of R, be a nonzero left ideal of R, F : R ! R be a generalized (; )-derivation and d : R ! Rbe an (; )-derivation. In the present paper we discuss the following situations: (i) F(xoy) = a(xy yx), (ii) F([x; y]) = a(xy yx), (iii) d(x)od(y) = a(xy yx) forall x; y 2 and a 2 f0; 1;ô€€€1g. Also some related results have been obtained.

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