Dual numbers (Q2915491)

Dual numbers were introduced in the 19th century by W. K. Clifford. They have many applications in kinematics, dynamics and differential geometry. This book presents algebraic structures on dual numbers and several generalizations of dual numbers. After a short introductory chapter, the authors develop the theory of dual number general rings in Chapter 2. These rings may also be rings of matrices or rings of polynomials. Higher dimensional dual numbers are introduced in Chapter 3. Their main properties are described in the same chapter. Other special types of dual numbers are defined in Chapter 4. They are interval dual numbers, fuzzy dual numbers, neutrosophic dual numbers and finite complex modulo integer neutrosophic dual numbers. Applications of the considered generalizations of dual numbers are discussed briefly in Chapter 5. The final chapter contains a list of 116 unsolved problem. Some of them are addressed to researchers in the area of dual numbers. The book is well-structured. The first three chapters provide basic concepts and they are suitable for undergraduates in mathematics. The rest of the chapters are intended for specialists in dual numbers and fuzzy models.