AbstractsMathematics

The indicated sum of a real scalar and a real or imaginary vector is called a scator. Either the scalar part or the vector part may be null. Scators generalize the complex variable to n-space. The algebra of scators is not generally associative under multiplication but the commutative and distributive laws are satisfied. A division algebra exists provided that division by a pure vector (except in the one dimensional case) is excluded. The basic laws of exponents are true excepting those for which the associative law does not hold. Exponential, trigonometric, hyperbolic and logarithmic functions are defined. All scators admit to an exponential representation and if the vector part is imaginary there exists a scator analog to DeMoivre's Theorem. The derivative of a scator with respect to a scator is defined in terms of differentials. The analogs to the Cauchy-Riemann equations of complex variables are derived.