Shahrood University of Technology Journal of Algebraic Systems 2345-5128 13 3 2025 11 01 RESULTS ON QUOTIENT NEAR-RINGS INVOLVING ADDITIVE MAPS 113 122 3129 10.22044/jas.2024.13603.1759 EN Abderrahmane Raji LMACS Laboratory, Faculty of Sciences and Technology, Sultan Moulay Slimane University, Beni Mellal, Morocco. Abdelkarim Boua Department of Mathematics, Polydisciplinary Faculty, LSI, Sidi Mohammed Ben Abdellah University, Taza, Morocco. Abdelilah Zerbane Department of Mathematics, Polydisciplinary Faculty, LSI, Sidi Mohammed Ben Abdellah University, Taza, Morocco. Journal Article 2023 09 22 We consider N to be a 3-prime field and P to be a prime ideal of N : In this paper, we study<br />the commutativity of the quotient ring N =P with left multipliers and derivations satisfying certain<br />identities on P, generalizing some well-known results in the literature. Furthermore, an example is<br />used to illustrate the necessity of our hypotheses Prime near-rings derivations left multipliers Commutativity https://jas.shahroodut.ac.ir/article_3129_ccb3f9c20056403238d9fbf7e23aaf2a.pdf