Advertisement

manuscripta mathematica

, Volume 95, Issue 1, pp 117–136 | Cite as

Rings with a theory of greatest common divisors

  • Friedemann Lucius
Article

Keywords

Finite Type Great Common Divisor Integral Closure Algebraic Extension Dedekind 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

6 Bibliography

  1. [1]
    Anderson, D. D./Mott, J./Zafrullah, M.: Some Quotient Based Statements in Multiplicative Ideal Theory. — Boll. Unione Mat. Ital., VII. Ser.,B 3 (1989), 456–476.Google Scholar
  2. [2]
    Aubert, Karl Egil: Divisors of finite character. — Ann. Mat. Pura Appl.38 (1983), 327–360.CrossRefGoogle Scholar
  3. [3]
    Becker, Ulrich: Kronecker-Divisoren und ggT-Theorie. Dipl. thesis. Math. Inst. der Georg-August-Universität Göttingen 1992 (unpubl.).Google Scholar
  4. [4]
    Borewicz, Senon I./Šafarevič, Igor R.: Zahlentheorie. — Basel/Stuttgart: Birkhäuser 1966.zbMATHGoogle Scholar
  5. [5]
    Bourbaki, Nicolas: Commutative Algebra. Chapters 1–7. — Berlin u.a.: Springer 1989.zbMATHGoogle Scholar
  6. [6]
    Geroldinger, A./Močkoř, J.: Quasi-divisor theories and generalizations of Krull domains. — J. Pure Appl. Algebra102 (1995), 289–311.zbMATHCrossRefGoogle Scholar
  7. [7]
    Gilmer, Robert: Multiplicative Ideal Theory. — Kingston (Ontario): Queen’s Papers 1992.Google Scholar
  8. [8]
    Jaffard, Paul: Systèmes Idéaux. — Paris: Dunod 1960.zbMATHGoogle Scholar
  9. [9]
    Kang, B. G.: Prüferv-Multiplication Domains and the RingR[X]Nu. — J. Algebra123 (1989), 151–170.zbMATHCrossRefGoogle Scholar
  10. [10]
    Koch, Helmut: Zur Begründung der Arithmetik in algebraischen Zahl und Funktionenkörpern. — Wiss. Z. Humboldt-Univ. Berlin. Math.-naturw. R.15 (1966), 187–189.Google Scholar
  11. [11]
    Koch, H.: Number Theory II. Algebraic Number Theory. (Encyclopedia of Mathematical Sciences 62) — Berlin u.a.: Springer 1992.Google Scholar
  12. [12]
    Kronecker, Leopold: Grundzüge einer arithmetischen Theorie der algebraischen Größen. — J. Reine Angew. Math.92 (1882), 1–122.Google Scholar
  13. [13]
    Krull, Wolfgang: Beiträge zur Arithmetik kommutativer Integritätsbereiche. II.v-Ideale und vollständig ganz abgeschlossene Integritätsbereiche. — Math. Z.41 (1936), 665–679.zbMATHCrossRefGoogle Scholar
  14. [14]
    Lucius, Friedemann: Ringe mit einer Theorie des größten gemeinsamen Teilers. — Math. Gottingensis, Heft7 (1997), 1–70.Google Scholar
  15. [15]
    Mott, Joe L./Zafrullah, Muhammad: On Prüferv-multiplication domains. — Manuscr. Math.26 (1981), 1–26.CrossRefGoogle Scholar
  16. [16]
    Močkoř, Jiří: Groups of Divisibility. — Dodrecht u.a.: Reidel 1983.Google Scholar
  17. [17]
    Močkoř, Jiři/Kontolatou, Angeliki: Groups with Quasi-divisors Theory. — Comment. Math. Univ. St. Pauli42 (1993), 23–36.Google Scholar
  18. [18]
    Prüfer, Heinz: Untersuchungen über Teilbarkeitseigenschaften in Körpern. — J. Reine Angew. Math.168 (1932), 1–36.zbMATHGoogle Scholar
  19. [19]
    Querre, Julien: Idéaux divisoriels d’un anneau de polynômes. — J. Algebra64 (1980), 270–284.zbMATHCrossRefGoogle Scholar
  20. [20]
    Skula, Ladislav: Divisorentheorie einer Halbgruppe. — Math. Z.114 (1970), 113–120.zbMATHCrossRefGoogle Scholar
  21. [21]
    Swan, R. G.:n-generator Ideals in Prüfer domains. — Pac. J. Math.111 (1984), 433–446.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Friedemann Lucius
    • 1
  1. 1.Mathematisches InstitutGeorg-August-Universität GöttingenGöttingen

Personalised recommendations