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Mat. Sb. (N.S.), 1978, Volume 105(147), Number 2, Pages 192–206 (Mi msb2525)  

This article is cited in 6 scientific papers (total in 6 papers)

Pure and finitely presentable modules, duality homomorphisms and the coherence property of a ring

E. G. Sklyarenko


Abstract: The homological properties of pure modules are considered, showing, in particular, that for coherent rings the pure modules occupy roughly the same position with respect to injective modules as the flat with respect to projective (for arbitrary rings). The duality homomorphisms $\operatorname{Tor}_p(A^*,F)\to\operatorname{Ext}^p(F,A)^*$ are examined in situations where they are not isomorphisms; dependence of the structure of these homomorphisms on the finite presentability or the purity of the modules $F$ and $A$, as well as on the coherence of the base ring, is studied. Characterizations of pure and flat modules in terms of duality, and characterizations of coherence, semihereditariness and noetherianness in terms of duality, purity and finite presentability are given.
Bibliography: 21 titles.

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English version:
Mathematics of the USSR-Sbornik, 1978, 34:2, 173–186

Bibliographic databases:

UDC: 512.7
MSC: Primary 16A52, 16A62; Secondary 16A33, 16A49, 16A60, 18G05, 18G20
Received: 27.10.1975 and 26.01.1977

Citation: E. G. Sklyarenko, “Pure and finitely presentable modules, duality homomorphisms and the coherence property of a ring”, Mat. Sb. (N.S.), 105(147):2 (1978), 192–206; Math. USSR-Sb., 34:2 (1978), 173–186

Citation in format AMSBIB
\Bibitem{Skl78}
\by E.~G.~Sklyarenko
\paper Pure and finitely presentable modules, duality homomorphisms and the coherence property of a~ring
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 105(147)
\issue 2
\pages 192--206
\mathnet{http://mi.mathnet.ru/msb2525}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=469977}
\zmath{https://zbmath.org/?q=an:0374.16022|0402.16022}
\transl
\jour Math. USSR-Sb.
\yr 1978
\vol 34
\issue 2
\pages 173--186
\crossref{https://doi.org/10.1070/SM1978v034n02ABEH001155}


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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. E. G. Sklyarenko, “Relative homological algebra in categories of modules”, Russian Math. Surveys, 33:3 (1978), 97–137  mathnet  crossref  mathscinet  zmath
    2. Alizade R., “Heredity of Coprojectivity and Coinjectivity for Some Proper Classes”, 4, no. 5, 1983, 3–7  mathscinet  isi
    3. Nieves Rodríguez Conzález, “On relative coherence and applications∗”, Communications in Algebra, 21:5 (1993), 1529  crossref
    4. Juan Rada, Manuel Saorin, “Rings characterized by (pre)envelopes and (pre)covers of their modules∗”, Communications in Algebra, 26:3 (1998), 899  crossref
    5. Garkusha G., “Relative Homological Algebra for the Proper Class Omega(F)”, Commun. Algebr., 32:10 (2004), 4043–4072  crossref  mathscinet  zmath  isi
    6. Pedro Nicolás, Manuel Saorín, “Classification of split torsion torsionfree triples in module categories”, Journal of Pure and Applied Algebra, 208:3 (2007), 979  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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