Welcome to Open Science
Contact Us
Home Books Journals Submission Open Science Join Us News
Bi-derivations on Semiprime Rings
Current Issue
Volume 3, 2015
Issue 5 (October)
Pages: 132-135   |   Vol. 3, No. 5, October 2015   |   Follow on         
Paper in PDF Downloads: 71   Since Sep. 8, 2015 Views: 1809   Since Sep. 8, 2015
Authors
[1]
Mehsin Jabel Atteya, Department of Mathematics, Al-Mustansiriyah University, College of Education, Baghdad, Iraq.
Abstract
The main purpose of this paper is studying and investigating some results concerning a symmetric bi-derivation D:R×R→R and d the trace of D ,on prime rings and semiprime rings R, where R admits for a symmetric bi-derivation D satisfying some conditions on R, (i). ([d(x),x]) n =0 for all x ∈R. (ii). D1 (d2 (x),x) n=0 holds for all x ∈R. (iii). (d1 (d2 (x))- f(x)) n=0 holds for all x ∈R. Where n be a positive integer and R be a 2-torsion and 3-torsion free.
Keywords
Symmetric Bi-derivation, Derivation, Central Mapping, Semiprime Rings, Prime Ring, Torsion Free
Reference
[1]
M. Ashraf, A. Ali and S. Ali, (σ-τ)-derivations on prime near-rings, Archivum Mathematicum (BRNO), Tomus 40(2004), 281-286.
[2]
H. E. Bell and G. Mason, On derivations in near, ring-near-ring and near-fields, North-Holland, Math. Studies 137(1987), 31-35.
[3]
M. Bresar, Commuting maps, a survey, Taiwanese J. Mathm.8 (2004), No.3, 361-397.
[4]
O. Golbasi, Some properties of prime near-rings with (σ-τ)-derivation, Siberian Mathematical Journal 46(2005), No.2, 270-275.
[5]
I. N. Herstein, Topics in ring theory, University of Chicago press, Chicago, 1969.
[6]
G. Maksa, On the trace of symmetric bi- derivations, C. R. Math. Rep. Sci. Canada 9(1987), 303-307.
[7]
M.A. Ozturk and Y.B. Jun, on generalized symmetric bi-derivations in primerings, East Asin Math. J. 15(1999), No. 2,165-176.
[8]
M. A. Ozturk and Y. B. Jun, on trace of symmetric bi-derivations in near-rings, Inter. J. Pure and Appl. Math. 7(2004), No.1, 95-102.
[9]
M. Sapanci, M. A. Ozturk and Y. B. Jun, Symmetric bi-derivations on prime rings, East Asian Math. J. 15(1999), No.1,105-109.
[10]
J. Vukman, Symmetric bi-derivations on prime and semiprime rings. Aequationes Math. 38(1989), 245-254.
[11]
J. Vukman, Two results concerning symmetric bi-derivation on prime ring, Aequationes Math., 40(1990), No.2-3, 181-189.
[12]
Yilmaz Ceven and Mehmet A.O., Some properties of symmetric bi-(σ-τ)-derivations in near-rings, Commun. Korean Math. Soc. 22(2007), No.4, 487-491.
[13]
H. E. Bell and W. S. Martindale III, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30 (1987), 92-10.
Open Science Scholarly Journals
Open Science is a peer-reviewed platform, the journals of which cover a wide range of academic disciplines and serve the world's research and scholarly communities. Upon acceptance, Open Science Journals will be immediately and permanently free for everyone to read and download.
CONTACT US
Office Address:
228 Park Ave., S#45956, New York, NY 10003
Phone: +(001)(347)535 0661
E-mail:
LET'S GET IN TOUCH
Name
E-mail
Subject
Message
SEND MASSAGE
Copyright © 2013-, Open Science Publishers - All Rights Reserved