Algebraic Properties of the Module of Slice Regular Functions in Several Quaternionic Variables

In this paper we define the notion of slice regularity for several quaternionic variables by employing the recent definition due to Ghiloni and Perotti in one variable [25]. We show that in the case of several variables slice regularity is equivalent to being solutions of intertwined Cauchy-Riemann type operators, and we give an algebraic treatment of these functions. We also sketch how to extend our ideas to the case of higher dimension.