Algebraic structure and basics of analysis of n-dimensional quaternionic space

In this study, we focused on n-dimensional quaternionic space $$ . To create the module structure, first part is devoted to define a metric depending on the product order relation of $$ . The set of $$ has been rewritten with a different representation of n-vectors. Using this notation, formulations corresponding to the basic operations in $$ are obtained. By adhering these representations, module structure of $$ over the set of real ordered n-tuples is given. Afterwards, we gave limit, continuity and the derivative basics of quaternion valued functions of a real variable.