On Prime and Semiprime Rings with Symmetric Generalized Biderivations

Auday H. Mahmood; Dheaa K. Hussain K. Hussein

doi:10.23851/mjs.v28i1.321

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.

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