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Multiplicative Ideal Theory in Commutative Algebra

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References

  1. Gilmer, R., Forty years of commutative ring theory. In: Facchini, A., Houston, E., and Salce, L. (ed) Rings, Modules, Algebras, and Abelian Groups. Lect. Notes Pure Appl. Math., 236. Dekker, New York 229–256 (2004)

    Google Scholar 

  2. Cahen, P.-J., Dimension de l’anneau des polynomes a valeurs entieres. manuscr. math., 67, 333–343 (1990)

    MathSciNet  Google Scholar 

  3. Cahen, P.-J. and Chabert, J.-L.: Integer-Valued Polynomials. Amer. Math. Soc. Surveys Monogr. No. 48. Providence, RI (1997)

    Google Scholar 

  4. Fontana, M., Izelgue, L., Kabbaj, S., and Tartarone, F., Polynomial closure in essential domains and pullbacks. Lect. Notes Pure Appl. Math. 205. Dekker, New York 307–321 (1999)

    Google Scholar 

  5. Fontana, M. and Kabbaj, S., Essential domains and two conjectures in dimension theory. Proc. Amer. Math. Soc., 132, 2529–2535 (2004)

    Article  MathSciNet  Google Scholar 

  6. Benhissi, A., Les Anneaux de Séries Formelles, Queen’s Papers Pure Appl. Math., 124, Kingston, Ont., Canada (2003)

    Google Scholar 

  7. Condo, J.T. and Coykendall, J., Strong convergence properties in SFTrings. Commun. Alg., 27, 2073–2085 (1999)

    MathSciNet  Google Scholar 

  8. Coykendall, J., The SFT-property does not imply finite dimension of power series rings. J. Algebra, 256, 85–96 (2002)

    Article  MathSciNet  Google Scholar 

  9. Kang, E.G. and Park, M.H., A localization of a power series ring over a valuation domain. J. Pure Appl. Alg., 140, 107–142 (1999)

    Article  MathSciNet  Google Scholar 

  10. Anderson, D.D., Kang, E.G., and Park, M.H., GCD-domains and power series rings. Commun. Alg., 30, 5955–5960 (2002)

    MathSciNet  Google Scholar 

  11. Eayart, M., Series formelles sur un anneau factorial. C.R. Acad. Sci. Paris Ser. A, 277, 449–450 (1973)

    MathSciNet  Google Scholar 

  12. Deckart, D. and Durst, L.K., Unique factorization in power series rings and semigroups. Pac. J. Math., 16, 239–242 (1966)

    Google Scholar 

  13. Lipman, J., Unique factorization in complete local rings. Proc. Symp. Pure Math., 29, 531–546 (1975)

    MathSciNet  Google Scholar 

  14. Samuel, P., On unique factorization domains. I11. J. Math., 5, 1–17 (1961)

    MathSciNet  Google Scholar 

  15. Zaks, A., Half-factorial domains. Israel J. Math., 37, 281–302 (1980)

    MathSciNet  Google Scholar 

  16. Podewski, K.-P., Minimale Ringe. Math.-Phys. Semesterber., 22, 193–197 (1973)

    MathSciNet  Google Scholar 

  17. Wagner, F.O., Minimal fields. J. Symbol. Logic, 65, 1833–1835 (2000)

    Article  Google Scholar 

  18. Claborn, L., Specified relations in the ideal class group. Mich. Math. J., 15, 249–255 (1968)

    Article  MathSciNet  Google Scholar 

  19. Geroldinger, A. and Göbel, R., Half-factorial subsets in infinite abelian groups. Houston J. Math., 29, 841–858 (2003)

    MathSciNet  Google Scholar 

  20. Narkiewicz, W., Elementary and Analytic Theory of Algebraic Numbers. Monografie Matematyczne No. 57, Polish Scientific Publishers (PWN), Warsaw (1974)

    Google Scholar 

  21. Anderson, D.D. and Anderson, D.F., Finite intersections of PID or factorial overrings. Canad. Math. Bull., 28, 91–97 (1985)

    MathSciNet  Google Scholar 

  22. Ershov, Y.I.: Multi-Valued Fields. Kluwer, New York (2001)

    MATH  Google Scholar 

  23. Gilmer, R., Two constructions of Prüfer domains. J. Reine Angew. Math., 239, 153–162 (1970)

    MathSciNet  Google Scholar 

  24. Gilmer, R. and Grams, A., Finite intersections of quotient rings of a Dedekind domain. J. London Math. Soc., 12, 257–261 (1976)

    MathSciNet  Google Scholar 

  25. Loper, K.A., On Prüfer non-D-rings. J. Pure Appl. Algebra, 96, 271–278 (1994)

    Article  MathSciNet  Google Scholar 

  26. Loper, K.A., Constructing examples of integral domains by intersecting valuation domains. In Non-Noetherian Commutative Ring Theory. Kluwer, Dordrecht 325–340 (2000)

    Google Scholar 

  27. Olberding, B., Holomorphy rings in function fields, this volume.

    Google Scholar 

  28. Schülting, H.-W., Über die Erzeugendenanzahl invertierbarer Ideale in Prüferringen, Comm. Alg., 7, 1331–1349 (1979)

    Google Scholar 

  29. Cahen, P.-J., Chabert, J.-L., and Loper, K.A., High dimension Prüfer domains of integer-valued polynomials, J. Korean Math. Soc., 38, 915–935 (2001)

    MathSciNet  Google Scholar 

  30. Chabert, J.-L., Un anneau de Prüfer, J. Algebra, 107, 1–16 (1987)

    Article  MathSciNet  Google Scholar 

  31. Chapman, S.T., Loper, K.A., and Smith, W.W., The strong two-generator property in rings of integer-valued polynomials determined by finite sets. Arch. Math. 78, 372–375 (2002)

    Article  MathSciNet  Google Scholar 

  32. Loper, A., A classification of all D such that Int(D) is a Prüfer domain, Proc. Amer. Math. Soc., 126, 657–660 (1998)

    Article  MathSciNet  Google Scholar 

  33. MacLane, S., A construction for absolute values. Trans. Amer. Math. Soc., 40, 363–395 (1936)

    Article  MathSciNet  Google Scholar 

  34. McQuillan, D., On Prüfer domains of polynomials, J. Reine Angew. Math., 358, 162–178 (1985)

    MathSciNet  Google Scholar 

  35. Swan, R., n-Generator ideals in Prüfer domains, Pac J. Math., 111, 433–446 (1984)

    MathSciNet  Google Scholar 

  36. Arnold, J.T., Gilmer, R., and Heinzer, W., Some countability conditions in a commutative ring. Ill. J. Math., 21, 648–665 (1977)

    MathSciNet  Google Scholar 

  37. Gilmer, R. and Heinzer, W., The quotient field of an intersection of integral domains, J. Algebra, 70, 238–249 (1981)

    Article  MathSciNet  Google Scholar 

  38. Gilmer, R. and Heinzer, W., On the cardinality of subrings of a commutative ring, Canad. Math. Bull., 29, 102–108 (1986)

    MathSciNet  Google Scholar 

  39. Heinzer, W., Noetherian intersections of integral domains II, Lecture Notes Math., 311, 107–119. Springer-Verlag, New York/Berlin (1973)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Florida State University, Tallahassee, FL, 32306-4510

    Robert Gilmer

Authors
  1. Robert Gilmer
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Editor information

Editors and Affiliations

  1. Florida Atlantic University, Boca Raton, Florida

    James W. Brewer

  2. University of Cennecticut, Storrs, Connecticut

    Sarah Glaz

  3. Purdue University, West Lafayette, Indiana

    William J. Heinzer

  4. New Mexico State University, Las Cruces, New Mexico

    Bruce M. Olberding

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Gilmer, R. (2006). Some questions for further research. In: Brewer, J.W., Glaz, S., Heinzer, W.J., Olberding, B.M. (eds) Multiplicative Ideal Theory in Commutative Algebra. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-36717-0_24

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