Annali di Matematica Pura ed Applicata

, Volume 123, Issue 1, pp 331–355

Topologically defined classes of commutative rings

  • Marco Fontana
Article

Sunto

In questo lavoro viene studiata l'operazione di somma amalgamata [13] di spazi spettrali [24] e vengono esaminate in dettaglio alcune proprietà algebriche degli anelli che interi vengono in tale operazione. Dei risultati ottenuti vengono poi fornite numerose applicazionalla teoria dei « D + m » domini diGilmer [19], a quella della seminormalizzazione diTra verso [38] e a quella delle CPI-estensioni nel senso diBoisen-Sheldon [5].

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References

  1. [1]
    S.Anantharaman,Schémas en groupes, espaces homogènes et espaces algébriques sur une base de dimension 1, Thèse, 1971.Google Scholar
  2. [2]
    A. Andreotti -E. Bombieri,Sugli omeomorfismi delle varietà algebriche, Ann. Sc. Norm. Sup. Pisa,23 (1969), pp. 430–450.Google Scholar
  3. [3]
    M. F. Atiyah -I. G. MacDonald,Introduction to commutative algebra, Addison-Wesley, Reading 1969.Google Scholar
  4. [4]
    C. E. Aull -W. J. Thron,Separation axioms between T 0 and T 1 Indag. Math.,24 (1962), pp. 26–37.Google Scholar
  5. [5]
    M. B. Boisen -P. B. Sheldon,CPI-extensions: overrings of integral domains with special prime spectrum, Canad. J. Math.,29 (1977), pp. 722–737.Google Scholar
  6. [6]
    N. Bourbaki,Algèbre commutative, Hermann, Paris, 1961–1965.Google Scholar
  7. [7]
    N. Bourbaki,Topologie générale, Ch. 1–4, Hermann, Paris 1971.Google Scholar
  8. [8]
    A.Bouvier - M.Fontana,Une classe d'espaces spectraux de dimension 1:les espaces principaux, (à paraître).Google Scholar
  9. [9]
    A. Conte,Proprietà di separazione della topologia di Zariski di uno schema, Rend. Ist. Lombardo A106 (1972), pp. 79–111.Google Scholar
  10. [10]
    J.Dieudonné,Topics in local algebra, Notre Dame Math. Lect. Notes, 1967.Google Scholar
  11. [11]
    D. E. Dobbs,On going down for simple overrings II, Comm. Algebra1 (1974), pp. 439–458.Google Scholar
  12. [12]
    D. E. Dobbs -I. J. Papick,On going down for simple overrings III, Proc. AMS,54 (1976), pp. 35–38.Google Scholar
  13. [13]
    J. Dugundji,Topology, Allyn and Bacon, Boston 1969.Google Scholar
  14. [14]
    S. Endô,Note on p.p. rings (a supplement to Hattori's paper), Nagoya Math. J.,17 (1960), pp. 167–170.Google Scholar
  15. [15]
    S. Endô,On semi-hereditary rings, J. Math. Soc. Japan,13 (1961), pp. 109–119.Google Scholar
  16. [16]
    S. Endô,Projective modules over polynomials rings, J. Math. Soc. Japan,15 (1963), pp. 339–395.Google Scholar
  17. [17]
    D.Ferrand,Conducteur, descente et pincement, Thèse.Google Scholar
  18. [18]
    M. Fontana -P. Maroscia,Sur les anneaux de Goldman, Boll. U.M.I.,13 B (1976), pp. 743–759.Google Scholar
  19. [19]
    R. Gilmer,Multiplicative ideal theory, Queen's Univ. Press, Kingston 1968.Google Scholar
  20. [20]
    R. Gilmer,A class of domains in which primary ideals are valuation ideals, Math. Ann.,161 (1965), pp. 247–254.Google Scholar
  21. [21]
    R. Gilmer -E. Bastida,Overrings and divisorial ideals of rings of the form D + M, Michigan Math. J.,20 (1974), pp. 79–95.Google Scholar
  22. [22]
    R. Gilmer -W. J. Heinzer,Intersections of quotient rings of an integral domain, J. Math. Kyoto Univ.,7 (1967), pp. 133–150.Google Scholar
  23. [23]
    A. Grothendieck -J. Dieudonne,Eléments de géométrie algébrique I, Springer, Berlin 1971.Google Scholar
  24. [24]
    M. Hochster,Prime ideal structure in commutative rings, Trans. AMS,142 (1969), pp. 46–60.Google Scholar
  25. [25]
    I. Kaplansky,Commutative rings, Allyn and Bacon, Boston 1970.Google Scholar
  26. [26]
    I. Kikuchi,Some remarkes on S-domains, J. Math. Kyoto Univ.,6 (1966), pp. 49–60.Google Scholar
  27. [27]
    W. J. Lewis,The spectrum of a rings as a partially ordered set, J. Algebra,25 (1973), pp. 419–434.Google Scholar
  28. [28]
    W. J. Lewis -J. Ohm,The ordering of Spec R, Canad. J. Math.,28 (1976), pp. 820–835.Google Scholar
  29. [29]
    P.Maroscia,Topological properties of some classes of G-domains, (to appear).Google Scholar
  30. [30]
    M. Nagata,Local rings, Interscience, New York 1962.Google Scholar
  31. [31]
    J. P. Olivier,Anneaux absolument plats universels et épimorphismes d'anneaux, C. R. Acad. Sci. Paris,266 (1968), pp. A317–318.Google Scholar
  32. [32]
    I. J. Papick,Topologically defined classes of going-down domains, Trans. AMS,219 (1976), pp. 1–37.Google Scholar
  33. [33]
    C. Pedrini,Incollamenti di ideali primi e gruppi di Picard, Rend. Sem. Mat. Univ. Padova,48 (1973), pp. 39–66.Google Scholar
  34. [34]
    R. L. Pendleton,A characterization of Q-domains, Bull. AMS,72 (1966), pp. 499–500.Google Scholar
  35. [35]
    G. Picavet,Sur les anneaux commutatifs dont tout idéal premier est de Goldman, C. R. Acad. Sci. Paris,280 (1975), pp. A 1719–1721.Google Scholar
  36. [36]
    R. Ramaswamy -T. M. Viswanathan,Overring properties of G-domains, Proc. AMS,58 (1976), pp. 59–66.Google Scholar
  37. [37]
    G. Tamone,Sugli incollamenti di ideali primi, Boll. U.M.I.,14 B (1977), pp. 810–825.Google Scholar
  38. [38]
    C. Traverso,Seminormality and Picard group, Ann. Sc. Norm. Sup. Pisa,24 (1970), pp. 585–595.Google Scholar

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© Fondazione Annali di Matematica Pura ed Applicata 1980

Authors and Affiliations

  • Marco Fontana
    • 1
  1. 1.Roma

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