Generalized Higher Derivations on Î“M-Modules

Auday Hekmat  Mahmood; Mahdi Saleh  Nayef; Salah Mehdi  Salih

doi:10.24996/ijs.2020.SI.1.6

Authors

Auday Hekmat Mahmood Depart of Mathematics College of education AL- Mustansiriyah University, Baghdad. Iraq
Mahdi Saleh Nayef Depart of Mathematics College of education AL- Mustansiriyah University, Baghdad. Iraq
Salah Mehdi Salih Depart of Mathematics College of education AL- Mustansiriyah University, Baghdad. Iraq

DOI:

https://doi.org/10.24996/ijs.2020.SI.1.6

Keywords:

generalized higher derivations, Jordan generalized higher derivations, Î“M-module

Abstract

The concepts of generalized higher derivations, Jordan generalized higher derivations, and Jordan generalized triple higher derivations on Î“-ring M into Î“M-modules X are presented. We prove that every Jordan generalized higher derivation of Î“-ring M into 2-torsion free Î“M-module X, such that aÎ±bÎ²c=aÎ²bÎ±c, for all a, b, c ïƒŽM and Î±,Î²ïƒŽÎ“, is Jordan generalized triple higher derivation of M into X.