Skip to main content
SpringerLink
Log in

Conducive integral domains as pullbacks

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. BARUCCI, On a class of Mori domains. Comm. Algebra11, 1989–2001, (1983)

    Google Scholar 

  2. V. BARUCCI - D.E. DOBBS, On chain conditions in integral domains. Can. Math. Bull. (to appear)

  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. N. BOURBAKI,Algèbre commutative. Hermann, Paris 1961–65

    Google Scholar 

  5. D.E. DOBBS, Divided rings and going-down. Pac. J. Math67, 353–363, (1976)

    Google Scholar 

  6. D.E. DOBBS - R. FEDDER, Conducive integral domains. J. Algebra (to appear)

  7. M. FONTANA, Topologically defined classes of commutative rings. Annali Mat. Pura Appl.123, 331–355, (1980)

    Google Scholar 

  8. M. FONTANA, Carrés cartesiens, anneaux divisés et anneaux localement divisés. Pre-Publ. Math. Univ. Paris-Nord, Fasc. 21, 1980

  9. R. GILMER,Multiplicative ideal theory, Queen's University, Kingston 1968

    Google Scholar 

  10. R. GILMER,Multiplicative ideal theory, Dekker, New York, 1972

    Google Scholar 

  11. R. GILMER - R.C. HEITMANN, On Pic (R[X]) for R sominormal. J. Pure Appl. Algebra16, 251–257, (1980)

    Google Scholar 

  12. A. GRAMS, Atomic rings and the ascending chain condition for principal ideals. Proc. Camb. Phil. Soc.75, 321–329, (1974)

    Google Scholar 

  13. A. GROTHENDIECK - J. DIEUDONNE,Eléments de géométrie algébrique I, Springer, Berlin 1971

    Google Scholar 

  14. J.R. HEDSTROM - E.G. HOUSTON, Pseudo-valuation domains, Pac. J. Math.75, 137–147, (1978)

    Google Scholar 

  15. W. HEINZER, Integral domains in which each non-zero ideal is divisorial. Mathematika15, 164–170, (1968)

    Google Scholar 

  16. J. QUERRE, Sur une propriété des anneaux de Krull. Bull. Sc. Math.95, 341–354, (1971)

    Google Scholar 

  17. N. RAILLARD, Sur les anneaux de Mori. Thèse, Univ. Pierre et Marie Curie, Paris VI, 1976

    Google Scholar 

  18. P. SHELDON, How changing D [[X]] changes its quotient field. Trans. AMS159, 223–244, (1971)

    Google Scholar 

  19. C. TRAVERSO, Seminortnality and Picard group. Ann. Sc. Norm. Sup. Pisa24, 585–595, (1970)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica Istituto “Guido Castelnuovo”, Universitá di Roma “La Sapienza”, 00185, Roma, Italia

    Valentina Barucci & Marco Fontana

  2. Department of Mathematics, University of Tennessee, 37996, Knoxville, Tennessee, USA

    David E. Dobbs

Authors
  1. Valentina Barucci
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David E. Dobbs
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marco Fontana
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Work performed under the auspices of GNSAGA of Consiglio Nazionale delle Ricerche and Dipartimento di Matematica, Università di Roma “La Sapienza”

Supported in part by grants from University of Tennessee Faculty Development Program and the Università di Roma “La Sapienza”

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barucci, V., Dobbs, D.E. & Fontana, M. Conducive integral domains as pullbacks. Manuscripta Math 54, 261–277 (1986). https://doi.org/10.1007/BF01171337

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01171337

Keywords

Search

Navigation