Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings

Ali Ibrahim Mansour^1,*, Amal A. Ibrahim¹, Auday Hekmat Mahmood¹

¹Department of Mathematics, College of  Education, Mustansiriyah University, Baghdad, Iraq

Emails: aliibrahimaltaay@uomustansiriyah.edu.iq; amal.ibrahim@uomustansiriyah.edu.iq; audaymath@uomustansiriyah.edu.iq

Abstract

Let  be the direct product of an associative ring . In the work the concepts of Endo Bi-Antiderivation, Jordan Endo Bi-Antiderivation and Quasi Endo Bi-Antiderivation on a ring  are introduced, furthermore the relations between these bi-additive mappings are given. As essential point, we searched for appropriate conditions that make equivalence between Jordan Endo Bi-Antiderivation and Quasi Endo Bi-Antiderivation. Also, we prove the same results for the generalized case of neutrosophic rings.

 Keywords: Direct product of ring; Prime rings; Bi-additive mapping; Neutrosophic ring