Algebraic properties of the module of slice regular functions in several quaternionic variables Fabrizio ColomboIrene SabadiniDaniela Struppa 30G3532A10algebraic analysisslice regular functionsquaternions 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 [R. Ghiloni and A. Perotti, \textit{Slice regular functions on real alternative algebras}, Adv. Math. \textbf{226} (2011), no. 2, 1662--1691]. 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. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4978 10.1512/iumj.2012.61.4978 en Indiana Univ. Math. J. 61 (2012) 1581 - 1602 state-of-the-art mathematics http://iumj.org/access/