Article in volume
Authors:
Radwan Mohammed Al-omary
Department of mathematics, Ibb ubiversity, Ibb, YEMEN.
email: raradwan959@gmail.com
S. Khalid Nauman
Department of Mathematics
Jinnah University for Women Karachi,\
Pakistan
email: synakhaled@hotmail.com
Title:
On prime rings with involution and generalized derivations
PDFSource:
Discussiones Mathematicae - General Algebra and Applications 43(1) (2023) 31-39
Received: 2020-10-30 , Revised: 2021-06-10 , Accepted: 2021-06-10 , Available online: 2022-11-29 , https://doi.org/10.7151/dmgaa.1404
Abstract:
In this note we investigate some commutativity conditions on prime rings
with involutions by using some generalized derivations. We have provided a
counter example as well.
Keywords:
$*$-ideals, involution, $*$-prime rings, derivations and generalized derivations
References:
- R.M. Al-omary and S.K. Nauman, Generalized derivations on prime rings satisfying certain identities, Commun. Korean Math. Soc. 36 (2) (2021) 229–238.
https://doi.org/10.4134/CKMS.c200227 - M. Ashraf and M.A Siddeeque, Certain differential identities in prime rings with involurion, Miskolc Math. Notes 16 (1) (2015) 33–44.
https://doi.org/10.18514/MMN.2015.1089 - M. Ashraf and M.R. Jamal, Generalized derivations on $*$-prime rings, Kyungpook Math. J. 58 (2018) 484–488.
https://doi.org/10.5666/KMJ.2018.58.3.481 - K. Emine and N. Rehman, Notes on generalized derivations of $\ast$-prime rings, Miskolc Math. Notes 1 (1) (2014) 117–123.
https://doi.org/10.18514/MMN.2014.779 - S.K. Nauman, N. Rehman and R.M. Al-Omary, Lie ideals, Morita context and generalized $(\alpha,\beta )$-derivations, Acta Math. Sci. 33 (4) (2011) 1059–1070.
https://doi.org/10.1016/S0252-9602(13)60063-6 - L. Oukhtite and S. Salhi, Commutativity of $\sigma$-prime rings, Glasnik Mathematicki 41 (2006) 57–64.
https://doi.org/10.3336/gm.41.1.05 - L. Oukhtite and S. Salhi, Derivations and commutativity of $\sigma$-prime rings, Int. J. Contept. Math. Sci. 1 (2006) 439–448.
- L. Oukhtite, S. Salhi and L. Taoufiq, Commutativity conditions on derivations and Lie ideals in $\sigma$-prime rings, Beitrage. Algebra. Geom. 51 (1) (2010) 275–282.
- M.R. Khan, D. Arora and M.A. Khan, $\sigma$-ideals and generalized derivation in $\sigma $-prime rings, Bol. Soc. Paran. Mat. 31 (2) (2012) 113–119.
https://doi.org/10.5269/bspm.v31i2.12119 - N. Rehman and O. Golbasi, Notes on $(\alpha ,\beta)$-generalized derivations of $\ast $-prime rings, Palestine J. Math. 5 (2) (2016) 258–269.
- N. Rehman, R.M. Al-Omary and A.Z. Ansari, On Lie ideals of prime rings with generalized derivations, Bol. Soc. Mat. Mex. 21 (1) (2015) 19–26.
https://doi.org/10.1007/s40590-014-0029-3 - N. Rehman and R.M. Al-Omary, On Commutativity of $2$-torsion free $\ast$-prime rings with Generalized Derivations, Mathematica 53 (2) (2011) 177–180.
- B.H. Shafee and S.K. Nauman, On extensions of right symmetric rings without identity, APM 4 (2014) 665–673.
https://doi.org/10.4236/apm.2014. 412075 - H. Shuliang, Generalized derivations of $\sigma$-prime rings, Int. J. Algebra 18 (2) (2008) 867–873.
Close