Abstract
A construction of Cohen-Macaulay modules over a polynomial ring arising in the study of the Cauchy-Fueter equations is extended from quaternions to arbitrary finite-dimensional associative algebras. It is shown for a certain class of algebras that this construction produces Cohen-Macaulay modules, and this class of algebras cannot be enlarged for a perfect base field. Several properties of this construction are also described. For the class of algebras under consideration several invariants of the resulting modules are calculated.
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