RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (1806 kB)
References: PDF file   HTML file

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

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} 

• http://mi.mathnet.ru/eng/msb2525
• http://mi.mathnet.ru/eng/msb/v147/i2/p192

 SHARE:

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
2. Alizade R., “Heredity of Coprojectivity and Coinjectivity for Some Proper Classes”, 4, no. 5, 1983, 3–7
3. Nieves Rodríguez Conzález, “On relative coherence and applications∗”, Communications in Algebra, 21:5 (1993), 1529
4. Juan Rada, Manuel Saorin, “Rings characterized by (pre)envelopes and (pre)covers of their modules∗”, Communications in Algebra, 26:3 (1998), 899
5. Garkusha G., “Relative Homological Algebra for the Proper Class Omega(F)”, Commun. Algebr., 32:10 (2004), 4043–4072
6. Pedro Nicolás, Manuel Saorín, “Classification of split torsion torsionfree triples in module categories”, Journal of Pure and Applied Algebra, 208:3 (2007), 979
•  Number of views: This page: 181 Full text: 51 References: 24