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

Area of Science:

• Mathematics
• Algebraic Structures
• Complex Analysis

Background:

• Quaternions are a fundamental number system with applications in various scientific fields.
• Understanding n-dimensional spaces is crucial for advanced mathematical and physical theories.

Purpose of the Study:

• To define a module structure for n-dimensional quaternionic space.
• To establish foundational concepts for quaternion-valued functions of a real variable.

Main Methods:

• Defining a metric based on the product order relation in n-dimensional quaternionic space.
• Representing n-vectors and deriving basic operations.
• Developing the module structure over real ordered n-tuples.

Main Results:

• A novel representation of n-vectors and their operations within the quaternionic space.
• The establishment of a module structure for n-dimensional quaternionic space.
• Introduction to limit, continuity, and derivative concepts for quaternion-valued functions.

Conclusions:

• The study successfully constructs a module structure for n-dimensional quaternionic space.
• This work provides essential tools for further research into quaternion analysis and its applications.