Orthogonal Derivations and Orthogonal Generalized Derivations on TM -Modules

Let M be r-ring and X be rM-module, Bresar and Vukman studied orthogonal derivations on semiprime rings. Ashraf and Jamal defined the orthogonal derivations on • -rings M. This research defines and studies the concepts of orthogonal derivation and orthogonal generalized derivations on rM -Module X and introduces the relation between the products of generalized derivations and orthogonality on rM -module. Mathematics Subject Classification: 16W30, 16W25, 16U80