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Abelian Groups and Modules pp 459–466Cite as

On a Class of Minimal Topological Modules

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Part of the book series: Mathematics and Its Applications ((MAIA,volume 343))

Abstract

We study minimality and total minimality of a class of topological modules over an arbitrary discrete ring.

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References

  1. W. W. Comfort and D. L. Grant, Cardinal invariants, pseudocompactness and minimality: some recent advances in the topological theory of topological groups, Topology Proc. 6, (1981), 227–265.

    MathSciNet  Google Scholar 

  2. D. Dikranjan, Minimal Topologies on Abelian Groups, Istituto di Algebra e Geometria dell’Università di Padova, Padua, Italy (1983).

    Google Scholar 

  3. D. Dikranjan and Iv. Prodanov, Totally minimal topological groups, Annuaire Univ. Sofia Fac. Math. Mec. 69, (1974/75), 5–11.

    Google Scholar 

  4. D. Dikranjan, Iv. Prodanov and L. Stoyanov, “Topological groups”, Pure and Applied Mathematics (E. Taft and Z. Nashed editors), Vol.130, Marcel Dekker Inc., New York-Basel, (1989).

    Google Scholar 

  5. D. Dikranjan and A. Tonolo, On the lattice of linear module topologies, Comm. Algebra 21(1), (1993), 275–298.

    Article  MathSciNet  MATH  Google Scholar 

  6. I. Kaplansky, “Infinite abelian groups”. Ann Arbor, Univ. of Mich. Press, (1954).

    Google Scholar 

  7. H. Leptin, Linear kompakten Moduln und Ringe I, II, Math. Z. 62–66 (1955)—(1957), 241–267, 289–327.

    Google Scholar 

  8. B. J. Müller, Duality theory for linearly topologized modules, Math. Z. 119, (1971), 63–74.

    Article  MathSciNet  MATH  Google Scholar 

  9. Iv. Prodanov, Minimal compact representations of algebras, Annuaire Univ. Sofia Fac. Math. Mec. 67, (1972/73), 507–542.

    Google Scholar 

  10. Iv. Prodanov, Precompact minimal topologies on some torsion-free modules, Annuaire Univ. Sofia Fac. Math. Mec. 68, (1973/74), 157–163.

    Google Scholar 

  11. Iv. Prodanov, Hensel modules, Pliska Stud. Math. Bulgar. 6, (1983), 23–46.

    MathSciNet  MATH  Google Scholar 

  12. Iv. Prodanov and L. Stoyanov, Minimal group topologies, Colloq. Math. Soc. Janos Bolyai 41, Topology Appl., Eger (Hungary), (1983), 493–508.

    Google Scholar 

  13. Iv. Prodanov and L. Stoyanov, Every minimal abelian group is precompact, C. R. Acad. Bulgare Sci. 37, (1984), 23–26.

    MathSciNet  MATH  Google Scholar 

  14. A. Tonolo, On the existence of a finest equivalent linear topology, Comm. Algebra 20(2), (1992), 437–455. Erratum ibid. 22(6), (1994), 23–17.

    Google Scholar 

  15. A. Tonolo, Denseness and Closedness with respect to Closure Operators, submitted to Journal of Pure and Applied Algebra.

    Google Scholar 

  16. P. Vámos, The dual of the notion of “finitely generated”, J. London Math. Soc. 43 S. I, (1968), 643–646.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica Pura ed Applicata, Università degli studi di Padova, Via Belzoni 7, Padova, Italy

    Alberto Tonolo

Authors
  1. Alberto Tonolo
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Informatics, University of Udine, Udine, Italy

    Alberto Facchini

  2. Department of Mathematics, University of Ferrara, Ferrara, Italy

    Claudia Menini

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© 1995 Springer Science+Business Media Dordrecht

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Tonolo, A. (1995). On a Class of Minimal Topological Modules. In: Facchini, A., Menini, C. (eds) Abelian Groups and Modules. Mathematics and Its Applications, vol 343. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0443-2_36

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  • DOI: https://doi.org/10.1007/978-94-011-0443-2_36

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4198-0

  • Online ISBN: 978-94-011-0443-2

  • eBook Packages: Springer Book Archive

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