manuscripta mathematica

, Volume 54, Issue 3, pp 261–277 | Cite as

Conducive integral domains as pullbacks

  • Valentina Barucci
  • David E. Dobbs
  • Marco Fontana


This article presents a characterization of conducive (integral) domains as the pullbacks in certain types of Cartesian squares in the category of commutative rings. Such squares behave well with respect to (semi)normalization, thus permitting us to recover the recent characterization by Dobbs-Fedder of seminormal conducive domains. The conducive domains satisfying various finiteness conditions (Noetherian, Archimedean, accp) are characterized by identifying suitable restrictions on the data in the corresponding Cartesian squares. Various necessary or sufficient conditions are given for Mori conducive domains. Consequently, one has examples of several (accp non-Mori; Mori non-Noetherian) conducive domains.


Number Theory Algebraic Geometry Topological Group Commutative Ring Integral Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    V. BARUCCI, On a class of Mori domains. Comm. Algebra11, 1989–2001, (1983)Google Scholar
  2. [2]
    V. BARUCCI - D.E. DOBBS, On chain conditions in integral domains. Can. Math. Bull. (to appear)Google Scholar
  3. [3]
    E. BASTIDA - R. GILMER, Overrings and divisorial ideals of rings of the form D+M. Michigan Math. J.20, 79–95, (1973)Google Scholar
  4. [4]
    N. BOURBAKI,Algèbre commutative. Hermann, Paris 1961–65Google Scholar
  5. [5]
    D.E. DOBBS, Divided rings and going-down. Pac. J. Math67, 353–363, (1976)Google Scholar
  6. [6]
    D.E. DOBBS - R. FEDDER, Conducive integral domains. J. Algebra (to appear)Google Scholar
  7. [7]
    M. FONTANA, Topologically defined classes of commutative rings. Annali Mat. Pura Appl.123, 331–355, (1980)Google Scholar
  8. [8]
    M. FONTANA, Carrés cartesiens, anneaux divisés et anneaux localement divisés. Pre-Publ. Math. Univ. Paris-Nord, Fasc. 21, 1980Google Scholar
  9. [9]
    R. GILMER,Multiplicative ideal theory, Queen's University, Kingston 1968Google Scholar
  10. [10]
    R. GILMER,Multiplicative ideal theory, Dekker, New York, 1972Google Scholar
  11. [11]
    R. GILMER - R.C. HEITMANN, On Pic (R[X]) for R sominormal. J. Pure Appl. Algebra16, 251–257, (1980)Google Scholar
  12. [12]
    A. GRAMS, Atomic rings and the ascending chain condition for principal ideals. Proc. Camb. Phil. Soc.75, 321–329, (1974)Google Scholar
  13. [13]
    A. GROTHENDIECK - J. DIEUDONNE,Eléments de géométrie algébrique I, Springer, Berlin 1971Google Scholar
  14. [14]
    J.R. HEDSTROM - E.G. HOUSTON, Pseudo-valuation domains, Pac. J. Math.75, 137–147, (1978)Google Scholar
  15. [15]
    W. HEINZER, Integral domains in which each non-zero ideal is divisorial. Mathematika15, 164–170, (1968)Google Scholar
  16. [16]
    J. QUERRE, Sur une propriété des anneaux de Krull. Bull. Sc. Math.95, 341–354, (1971)Google Scholar
  17. [17]
    N. RAILLARD, Sur les anneaux de Mori. Thèse, Univ. Pierre et Marie Curie, Paris VI, 1976Google Scholar
  18. [18]
    P. SHELDON, How changing D [[X]] changes its quotient field. Trans. AMS159, 223–244, (1971)Google Scholar
  19. [19]
    C. TRAVERSO, Seminortnality and Picard group. Ann. Sc. Norm. Sup. Pisa24, 585–595, (1970)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Valentina Barucci
    • 1
  • David E. Dobbs
    • 2
  • Marco Fontana
    • 1
  1. 1.Dipartimento di Matematica Istituto “Guido Castelnuovo”Universitá di Roma “La Sapienza”RomaItalia
  2. 2.Department of MathematicsUniversity of TennesseeKnoxvilleUSA

Personalised recommendations