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

O. N. Popov

M. V. Lomonosov Moscow State University

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.

UDC: 512.715/.717+512.552.22

MSC: Primary 13C14, 16G10; Secondary 13B25

Received: 15.10.2003

DOI: 10.4213/sm846

 English version: Sbornik: Mathematics, 2004, 195:9, 1309–1319

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