  This is an English translation of the author's Ph.D. thesis, accumulating his
results on a construction of Cohen-Macaulay modules over a polynomial ring that
appeared in the study of Cauchy-Fueter equations. This construction is
generalized from quaternions to arbitrary finite-dimensional associative
algebras. We show that for maximally central algebras (as introduced by
Azumaya) this construction produces Cohen-Macaulay modules and is an exact
functor (tensoring with a bimodule, actually) and this class of algebras cannot
be enlarged. For this class several invariants of the resulting modules are
calculated via a fairly explicit description of their graded minimal free
resolution, that is constructed from the Eagon-Northcott complex. These results
have been published in Russ. Math. Surveys and Sbornik: Mathematics but for
some proofs, a concise and complete exposition is presented here.
