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Mat. Sb. (N.S.), 1970, Volume 83(125), Number 2(10), Pages 222–233 (Mi msb3509)  

This article is cited in 8 scientific papers (total in 8 papers)

Homological dimension of Banach algebras of analytic functions

A. Ya. Helemskii


Abstract: In this article we calculate the homological dimensions of a certain class of Banach modules over algebras with uniform convergence. The scheme proposed allows us, in particular, to find the homological dimension of all one-dimensional modules over Banach algebras of functions holomorphic on a polydisk and on a ball in $\mathbf C^n$.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1970, 12:2, 221–233

Bibliographic databases:

UDC: 517.53+513.881
MSC: 18G20, 46J10, 46E50, 46J20, 16S37, 18A30
Received: 25.12.1969

Citation: A. Ya. Helemskii, “Homological dimension of Banach algebras of analytic functions”, Mat. Sb. (N.S.), 83(125):2(10) (1970), 222–233; Math. USSR-Sb., 12:2 (1970), 221–233

Citation in format AMSBIB
\Bibitem{Hel70}
\by A.~Ya.~Helemskii
\paper Homological dimension of Banach algebras of analytic functions
\jour Mat. Sb. (N.S.)
\yr 1970
\vol 83(125)
\issue 2(10)
\pages 222--233
\mathnet{http://mi.mathnet.ru/msb3509}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=271736}
\zmath{https://zbmath.org/?q=an:0202.41501}
\transl
\jour Math. USSR-Sb.
\yr 1970
\vol 12
\issue 2
\pages 221--233
\crossref{https://doi.org/10.1070/SM1970v012n02ABEH000918}


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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. A. Ya. Helemskii, “The torsion product of modules over Banach algebras”, Funct. Anal. Appl., 5:1 (1971), 84–86  mathnet  crossref  mathscinet  zmath
    2. A. Ya. Helemskii, “Homological methods in Taylor's holomorphic calculus of several operators in a Banach space”, Russian Math. Surveys, 36:1 (1981), 139–192  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. L. I. Pugach, “On the homological dimension of Banach algebras of smooth functions”, Russian Math. Surveys, 37:4 (1982), 135–136  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. L. I. Pugach, “Homological dimension of ideals of functional algebras and analytic structure”, Funct. Anal. Appl., 16:3 (1982), 227–228  mathnet  crossref  mathscinet  zmath  isi
    5. L. I. Pugach, “Proektivnye idealy banakhovykh algebr i approksimativnye edinitsy”, Fundament. i prikl. matem., 1:4 (1995), 1119–1123  mathnet  mathscinet  zmath
    6. Bade W. Dales H. Lykova Z., “Algebraic and Strong Splittings of Extensions of Banach Algebras”, Mem. Am. Math. Soc., 137:656 (1999), 1+  isi
    7. Ermert O., “Hochschild Cohomology Groups of Certain Algebras of Analytic Functions with Coefficients in One-Dimensional Bimodules”, Studia Math., 137:1 (1999), 1–31  isi
    8. Yu. V. Selivanov, “Lower bounds for homological dimensions of Banach algebras”, Sb. Math., 198:9 (2007), 1351–1377  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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