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This book consists of two chapters, in chapter one we reviewed some known definitions and some necessary lemmas which it used in the next chapters. Chapter two consists of four sections: In section one we defined and studied the concepts of (s, )-homomorphism, Jordan (s, )-homomorphism and Jordan triple (s, )- homomorphism on prime ring R . In section two we introduced the concepts of generalized (s, )-homomorphism and generalized Jordan (s, )-homomorphism and we studied these concepts on prime ring R . In section three we defined and studied the concepts of (s, )-higher homomorphism, Jordan (s, )-higher homomorphism and Jordan triple (s, )-higher homomorphism. The main objective of section three is to prove a Jordan (s, )-higher homomorphism from a ring R into 2-torsion free ring R', such that and si i = i si is a Jordan triple (s, )-higher homomorphism. In section four the main objective proved that every generalized Jordan (s, )-higher homomorphism of a ring R into prime ring R' is either generalized (s, )-higher homomorphism or (s, )- higher anti homomorphism.
About the author
Fawaz Raad Jarullah i was born in Iraq - Baghdad -1982 ,i completed my university studies in the Baghdad University ,College of Education Pure Sciences Ibn Al-Haytham in 2004,i got a Master of Science in mathematics from , Al-Mustansirya University , College of Education , i have many research in non commutative algebra in web .
