### Regular Functions with Values in a Noncommutative Algebra using Clifford Analysis

#### Abstract

We construct a noncommutative algebra C(2) that is a subalgebra of the Pauli matrices of M(2;C), and investigate the properties of solutions with values in C(2) of the inhomogeneous Cauchy-Riemann system of partial differential equations with coefficients in the associated Pauli matrices. In addition, we construct a commutative subalgebra C(4) of M(4;C), obtain some properties of biregular functions with values in C(2) on Ω in C^2 × C^2, define a J-regular function of four complex variables with values in C(4), and examine some properties of J-regular functions of partial differential equations.

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