Modules over a polynomial ring obtained from representations of finite-dimensional associative algebras

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.