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Mat. Sb., 2002, Volume 193, Number 3, Pages 115–134 (Mi msb639)  

This article is cited in 3 scientific papers (total 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.

DOI: https://doi.org/10.4213/sm639

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

Bibliographic databases:

UDC: 512.715/717+512.552.22
MSC: Primary 13C14; Secondary 13D25, 13C15
Received: 24.05.2001

Citation: O. N. Popov, “Modules over a polynomial ring obtained from representations of finite-dimensional associative algebras”, Mat. Sb., 193:3 (2002), 115–134; Sb. Math., 193:3 (2002), 423–443

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. N. Popov, “More about a construction for modules over a polynomial ring”, Russian Math. Surveys, 58:2 (2003), 381–383  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. O. N. Popov, “On a construction of modules over a polynomial ring in the case of an arbitrary field”, Russian Math. Surveys, 59:3 (2004), 583–584  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. 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  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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