Some algebraic identities in 3-prime near-rings

In this paper, we study the commutativity of 3-prime near-rings satisfying some differential identities on Jordan ideals involving certain additive maps.Some well-known results characterizing the commutativity of 3-prime nearrings by derivations and left multipliers are extended to right multipliers and left generalized derivations.Furthermore, an example is given showing the necessity of the 3-primeness mentioned in the assumptions of our theorems is given.RSUM.Dans ce travail, nous tudions la commutativit des quasi-anneaux 3-premiers satisfaisant certaines identits diffrentielles sur des idaux de Jordan impliquant certaines applications additives.Certains rsultats bien connus caractrisant la commutativit des quasi-anneaux 3-premiers par l'action des drivations et des multiplicateurs gauche ont t tendus aux multiplicateurs droite et aux drivations gnralises gauche.De plus, nous avons enrichi cet article par un exemple qui montre la ncessit de la 3-primalit mentionne dans les hypothses de nos thormes.