This article is cited in 3 papers

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

O. N. Popov

M. V. Lomonosov Moscow State University

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.

UDC: 512.715/717+512.552.22

MSC: Primary 13C14; Secondary 13D25, 13C15

Received: 24.05.2001

DOI: 10.4213/sm639

 English version: Sbornik: Mathematics, 2002, 193:3, 423–443

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