On modules over a polynomial ring obtained from representations of finite-dimensional associative algebras. II. The case of a non-perfect field

Abstract

The author's earlier results on the construction of Cohen-Macaulay modules over a polynomial ring that emerged in the study of Cauchy-Fueter equations and was generalized by him from the quaternions to arbitrary finite-dimensional associative algebras are extended to the case of algebras over a non-perfect field. Namely, it is proved that for maximally central algebras (introduced by Azumaya) the resulting modules are Cohen-Macaulay, this construction has other good properties, and this class cannot be enlarged. The calculations of various invariants of the resulting modules in the case of a perfect field remain valid.