On Prime and Semiprime Rings with Symmetric Generalized Biderivations
Keywords:Prime rings, Semiprime rings, symmetric generalized Biderivations, traces of biadditive maps.
AbstractThe 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.
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.
How to Cite
The journal has no restrictions for the author to hold the copyrights of his articles. The journal does not allow authors to republish the same article in other journals or conferences that is published in one of its volumes.