scholarly journals The commutativity in prime Gamma rings with left derivation

2007 ◽  
Vol 2 ◽  
pp. 103-108
Author(s):  
M. Asci ◽  
S. Ceran
Keyword(s):  
Left Derivation ◽  
Gamma Rings

Gamma-rings and ncrita equivalence

1984 ◽  
Vol 12 (14) ◽  
pp. 1781-1786 ◽  
Author(s):  
N. Parvathi ◽  
P.A. Rajendran
Keyword(s):  
Gamma Rings

scholarly journals On Jordan left $k$-derivations of completely prime $\Gamma$-rings

2010 ◽  
Vol 40 (6) ◽  
pp. 1829-1840
Author(s):  
Sujoy Chakraborty ◽  
Akhil Chandra Paul
Keyword(s):  
Gamma Rings

scholarly journals Inner Derivations on Semiprime Gamma Rings

2019 ◽  
Vol 39 ◽  
pp. 101-110
Author(s):  
Sujoy Chakraborty ◽  
Md Mahbubur Rashid ◽  
Akhil Chandra Paul
Keyword(s):  
Gamma Rings

We study inner derivations and generalized inner derivations in semiprime Γ-rings to develop some important results. If f and g are inner derivations of a semiprime Γ-ring M satisfying the equation  for all , then we show that . This equation produces a number of results on generalized inner derivations as well. GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 101-110

scholarly journals Semi derivations of prime gamma rings

2012 ◽  
Vol 31 ◽  
pp. 65-70
Author(s):  
Kalyan Kumar Dey ◽  
Akhil Chandra Paul
Keyword(s):  
Prime Ring ◽  
Additive Mapping ◽  
Prime Rings ◽  
Subject Classifications ◽  
Associated Function ◽  
Gamma Rings

Let M be a prime ?-ring satisfying a certain assumption (*). An additive mapping f : M ? M is a semi-derivation if f(x?y) = f(x)?g(y) + x?f(y) = f(x)?y + g(x)?f(y) and f(g(x)) = g(f(x)) for all x, y?M and ? ? ?, where g : M?M is an associated function. In this paper, we generalize some properties of prime rings with semi-derivations to the prime &Gamma-rings with semi-derivations. 2000 AMS Subject Classifications: 16A70, 16A72, 16A10.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10309GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 65-70

Commutators in semiprime gamma rings

2019 ◽  
Vol 13 (04) ◽  
pp. 2050078
Author(s):  
Ahmad Al Khalaf ◽  
Iman Taha ◽  
Orest D. Artemovych
Keyword(s):  
Gamma Rings

We characterize connections between associative, Lie and Jordan structures of semiprime gamma rings.

scholarly journals On Jordan left-I-centralizers of prime and semiprime gamma rings with involution

2016 ◽  
Vol 24 (1) ◽  
pp. 8-14
Author(s):  
Kalyan Kumar Dey ◽  
Akhil Chandra Paul ◽  
Bijan Davvaz
Keyword(s):  
Rings With Involution ◽  
Gamma Rings

scholarly journals Regular gamma rings

1987 ◽  
Vol 11 (2) ◽  
pp. 371-382 ◽  
Author(s):  
Shoji Kyuno ◽  
Nobuo Nobusawa ◽  
Mi-Soo B.Smith
Keyword(s):  
Gamma Rings

scholarly journals Generalized Derivations in Semiprime Gamma Rings

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Kalyan Kumar Dey ◽  
Akhil Chandra Paul ◽  
Isamiddin S. Rakhimov
Keyword(s):  
Generalized Derivation ◽  
Additive Mapping ◽  
Generalized Derivations ◽  
Gamma Rings ◽  
Torsion Free

LetMbe a 2-torsion-free semiprimeΓ-ring satisfying the conditionaαbβc=aβbαcfor alla,b,c∈M,  α,β∈Γ, and letD:M→Mbe an additive mapping such thatD(xαx)=D(x)αx+xαd(x)for allx∈M,  α∈Γand for some derivationdofM. We prove thatDis a generalized derivation.

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

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