Advertisement

Ukrainian Mathematical Journal

, Volume 66, Issue 2, pp 317–321 | Cite as

A Sharp Bézout Domain is an Elementary Divisor Ring

  • B. V. Zabavs’kyi
Article

We prove that a sharp Bézout domain is an elementary divisor ring.

Keywords

Maximum Ideal Arbitrary Element Formal Power Series Prime Ring Minimal Ideal 
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.

References

  1. 1.
    R. Gilmer, “Overrings of Prufer domains,” J. Algebra, 4, 331–340 (1966).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    R. Gilmer and W. Heinzer, “Overrings of Prufer domains II,” J. Algebra, 7, 281–302 (1967).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    I. Kaplansky, “Elementary divisors and modules,” Trans. Amer. Math. Soc., 66, 464–491 (1949).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    M. Larsen, W. Levis, and T. Shores, “Elementary divisor rings and finitely presented modules,” Trans. Amer. Math. Soc., 187, No. 1, 231–248 (1974).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    B. Olberding, “Globalizing local properties of Prufer domains,” J. Algebra, 20, 480–504 (1998).MathSciNetCrossRefGoogle Scholar
  6. 6.
    B. Zabavsky, “Fractionally regular Bezout ring,” Mat. Stud., 32, 70–80 (2009).MathSciNetGoogle Scholar
  7. 7.
    O. Zariski and P. Samuel, Commutative Algebra, Vol. 1, Van Nostrand, Princeton (1958).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • B. V. Zabavs’kyi
    • 1
  1. 1.Franko Lviv National UniversityLvivUkraine

Personalised recommendations