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manuscripta mathematica

, Volume 57, Issue 1, pp 109–124 | Cite as

The ascending chain condition for real ideas

  • Paulo Ribenboim
Article
  • 37 Downloads

Abstract

If A is a ring satisfying the ascending chain condition for real ideals, then this condition is also satisfied by the polynomial ring A[X]. However, an example is given to illustrate that the condition need not to hold in the power series ring A[[X]]. It is also shown that if every real prime ideal is the real ideal generated by finitely many elements, then the ring satisfies the ascending chain condition for real ideals. So, the analogues of Hilbert basis theorem and Cohen's theorem hold for real ideals.

Keywords

Power Series Number Theory Algebraic Geometry Prime Ideal Topological Group 
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.

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References

  1. [1]
    LAM, T.Y.: Introduction to real algebra. Rocky Mtn. J.14, 767–814 (1984)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Paulo Ribenboim
    • 1
  1. 1.Department of MathematicsQueen's UniversityKingstonCanada

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