Prime Ideals That Satisfy Hensel’s Lemma

Chapter

Abstract

Nagata proved that (R, P) is a Henselian domain if and only if every integral extension domain of R is quasi-local. We explore, with partial success, how to generalize that result.

Keywords

Henselian Prime ideals Integral extensions Integral domains 

Subject Classifications:

13A15 13B22 13G05 13J15 

References

  1. 1.
    W. Heinzer, D. Lantz, Factorization of Monic polynomials. Proc. Am. Math. Soc. 131, 1049–1052 (2003)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    W. Heinzer, S. Wiegand, Prime ideals in two-dimensional polynomial rings. Proc. Am. Math. Soc. 107, 577–586 (1989)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    I. Kaplansky, Commutative Rings (University of Chicago Press, Chicago, 1974)MATHGoogle Scholar
  4. 4.
    S. McAdam, Going down and open extensions. Can. J. Math 27, 111–114 (1975)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    S. McAdam, Strongly comaximizable primes. J. Algebra 170, 206–228 (1994)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    N. Nagata, Local Rings (Interscience, New York, 1962)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Mathematics Department, RLM 8.100The University of Texas at AustinAustinUSA

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