On Prime and Semiprime Rings with Symmetric Generalized Biderivations

Authors

  • Auday H. Mahmood Department of Mathematics, College of Education, Mustansiriyah University
  • Dheaa K. Hussain K. Hussein Department of Mathematics, College of Education, Mustansiriyah University

DOI:

https://doi.org/10.23851/mjs.v28i1.321

Keywords:

Prime rings, Semiprime rings, symmetric generalized Biderivations, traces of biadditive maps.

Abstract

The propose of this paper is to present some results concerning the symmetric generalized Biderivations when their traces satisfies some certain conditions on an ideal of prime and semiprime rings. We show that a semiprime ring R must have a nontrivial central ideal if it admits appropriate traces of symmetric generalized Biderivations, under similar hypothesis we prove commutativity in prime rings.

References

Bres ̆ar M., Centralizing Mapping and Derivations in Prime Rings, J. Algebra 156, 385-394, 1991.

Maksa G., Remark on symmetric biadditive functions having non-negative diagonalization, Glasnik Math. 15 279-280, 1980.

Maksa G., On the trace of Symmetric bi-derivations, C. R. Math. Rep. Acad. Sci. Canada 9, 303-307, 1987.

Vukman J., Symmetric Bi-derivations on Prime and Semiprime Rings, AEquationes Mathematicae, Vol. 38, 245-254, 1989. CrossRef

Argac N., On prime and semiprime rings with Deriavations, Algebra Colloq. 13 (3), 371.380, 2006.

Ceven M.Y., and O ̈ztu ̈rk M. A., Some properties of symmetric Bi-(σ,τ)-Derivations in Near-Rings, Commun. Korean Math. Soc. 22, No. 4, 487-491, 2007. CrossRef

Auday H. M., On Generalized Bi deriavations and relatead additive mappings, Ph.D. Thesis, Mustansiriyah University, Iraq, 2015.

Glbasi O. and Aydin N., Some results on Endomorphisms of prime ring which are (σ, τ) -derivation, East Asian Math. J. 18, 33-41, 2002.

Zalar B., On centralizers of semiprime rings, Comment. Math. Univ. Carolinae, 32, 4 609-614, 1991.

Herestein I. N., Rings with involution, The University of Chicago Press, Chicago, Amer., 1976.

Ali A., Filippis D. and Shujat F., Results Concerning Symmetric Generalized Biderivation of Prime and Semiprime Rings, Mathematical Bechak, 66 (4), 410-417, 2014.

Downloads

Published

2017-11-19

How to Cite

[1]
A. H. Mahmood and D. K. H. K. Hussein, “On Prime and Semiprime Rings with Symmetric Generalized Biderivations”, MJS, vol. 28, no. 1, pp. 112–117, Nov. 2017.

Issue

Section

Mathematics