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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.
Received: 15.10.2003
Citation:
O. N. Popov, “On modules over a polynomial ring obtained from representations of finite-dimensional associative algebras. II. The case of a non-perfect field”, Sb. Math., 195:9 (2004), 1309–1319
Linking options:
https://www.mathnet.ru/eng/sm846https://doi.org/10.1070/SM2004v195n09ABEH000846 https://www.mathnet.ru/eng/sm/v195/i9/p75
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