Annali di Matematica Pura ed Applicata

, Volume 113, Issue 1, pp 211–235 | Cite as

Dualità per alcune classi di moduliE-compatti

  • Adalberto Orsatti


Starting from a topological module E over a commutative discrete ring A, the category C(E) of E-compact modules is defined as the class of all A-modules topologically isomorphic to closed submodules of direct product of copies of E. Under suitable assumptions it is shown that C(E) is dual of the category of abstract A-modules M for whichHomA(M, E) separates points of M. The duality theory so obtained contains as particular cases Pontryagin's duality between discrete and compact abelian groups and Macdonald's duality between lineary discrete and linearly compact modules over a complete local ring. There are also some applications to the theory of linearly compact modules over noetherian rings.


  1. [1]
    N. Bourbaki,Topologie Générale, Cap. 7, Paris (1963).Google Scholar
  2. [2]
    N. Bourbaki,Algebre Commutative, Cap. 3, Paris (1961).Google Scholar
  3. [3]
    S. Fakhruddin,Linearly compact modules over noetherian rings, J. of Algebra,24 (1973), pp. 554–550.CrossRefMathSciNetGoogle Scholar
  4. [4]
    J. Kelley,General Topology, New York (1955).Google Scholar
  5. [5]
    I. Macdonald,Duality over complete local rings, Topology,1 (1962), pp. 213–235.CrossRefzbMATHMathSciNetGoogle Scholar
  6. [6]
    E. Matlis,Injective modules over noetherian rings, Pac. J. of Math.,8 (1958), pp. 511–528.zbMATHMathSciNetGoogle Scholar
  7. [7]
    E. Matlis,Modules with descending chain condition, T.A.M.S.,97 (1960), pp. 495–508.CrossRefMathSciNetGoogle Scholar
  8. [8]
    C. NĂstĂsescu -T. Albu,Decomposition primaire des modules, J. of Algebra,23 (1972), pp. 263–270.CrossRefGoogle Scholar
  9. [9]
    L. Pontryagin,Topological Groups, New York (1966).Google Scholar
  10. [10]
    B. Stenström,Rings and modules of quotientes, Lecture Notes n. 237, Berlin (1971).Google Scholar
  11. [11]
    D. Zelinsky,Linearly compact modules and rings, Am. J. of Math.,75 (1953), pp. 79–90.zbMATHMathSciNetGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1977

Authors and Affiliations

  • Adalberto Orsatti
    • 1
  1. 1.Padova

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