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Zapiski Nauchnykh Seminarov POMI, 2001, Volume 281, Pages 186–209 (Mi znsl1495)  

This article is cited in 1 scientific paper (total in 1 paper)

Continuous functors and duality

M. B. Zvyagina

Saint-Petersburg State University
Full-text PDF (283 kB) Citations (1)
Abstract: Let $\Lambda$ be an associative ring with unity and let ${}_\Lambda\mathfrak M$ be a category of left unitary $\Lambda$-modules. The complete characterization of continuous additive co- and contravariant functors ${}_\Lambda\mathfrak M\to_\mathbb Z\mathfrak M$ is given. Such functors are either representable, or equivalent to a tenzor product, or the trivial functor. The class of categories, which are dual to ${}_\Lambda\mathfrak M$ and thefore equivalent to the category of compact right $\Lambda$-modules, is constructed by purely algebraic means. The canonical category is extracted from this class. The purely algebraic structure is constructed that is equivalent to the topology-algebraic structure of compact right $\Lambda$-module. Algebraic equivalents of connectivity and of complete inconnectivity are given.
Received: 21.06.2001
English version:
Journal of Mathematical Sciences (New York), 2004, Volume 120, Issue 4, Pages 1591–1602
DOI: https://doi.org/10.1023/B:JOTH.0000017888.30739.7a
Bibliographic databases:
UDC: 512.58
Language: Russian
Citation: M. B. Zvyagina, “Continuous functors and duality”, Problems in the theory of representations of algebras and groups. Part 8, Zap. Nauchn. Sem. POMI, 281, POMI, St. Petersburg, 2001, 186–209; J. Math. Sci. (N. Y.), 120:4 (2004), 1591–1602
Citation in format AMSBIB
\Bibitem{Zvy01}
\by M.~B.~Zvyagina
\paper Continuous functors and duality
\inbook Problems in the theory of representations of algebras and groups. Part~8
\serial Zap. Nauchn. Sem. POMI
\yr 2001
\vol 281
\pages 186--209
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1495}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1875724}
\zmath{https://zbmath.org/?q=an:1070.16004}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2004
\vol 120
\issue 4
\pages 1591--1602
\crossref{https://doi.org/10.1023/B:JOTH.0000017888.30739.7a}
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  • https://www.mathnet.ru/eng/znsl/v281/p186
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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