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In this article we show that it is possible to construct a Koszul-type complex for maps given by suitable pairwise commuting matrices of polynomials. This result has applications to surjectivity theorems for constant coefficients differential operators of finite and infinite order. In particular, we construct a large class of constant coefficients differential operators which are surjective on the space of regular (or monogenic) functions on open convex sets. [ABSTRACT FROM AUTHOR]

In this article some generalizations to eight dimensional real algebras of the notion of Cauchy-Fueter regularity are introduced, by defining suitable operators. Some properties of the nullsolutions of those operators such as removability of compact singularities are studied and the analogue of the Cauchy formula is provided. Special attention is devoted to the case of regularity in the Clifford algebra on three units. [ABSTRACT FROM AUTHOR]