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Let M be a Hilbert C -module. A linear mapping dW M! M is called a deriva- tion if d. ·/D ·C ·C d· for all x;y;·2 M. We give some results for derivations and automatic continuity of them on M. Also, we will characterize generalized derivations and strong higher derivations on the algebra of compact operators and adjointable operators of HilbertC -modules, respectively. 2010 Mathematics Subject Classification: 46L08; 16W25

Kinds of derivations on Hilbert $C^*$-modules and their operator algebras