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Difference between revisions of "Prime ideal theorem"

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The assertion that every ideal in a [[Boolean algebra]] can be extended to a prime ideal.  It is a consequence of the [[Axiom of Choice]], but is known to be strictly weaker.  It implies the [[Tikhonov theorem]] for Hausdorff spaces.
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The assertion that every ideal in a [[Boolean algebra]] can be extended to a prime ideal.  It is a consequence of the [[Axiom of choice]], but is known to be strictly weaker.  It implies the [[Tikhonov theorem]] for Hausdorff spaces.
  
 
====References====
 
====References====
* T. Jech, "Set theory. The third millennium edition, revised and expanded" Springer Monographs in Mathematics (2003). ISBN 3-540-44085-2 {{ZBL|1007.03002}}
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* T. Jech, "Set theory. The third millennium edition, revised and expanded" Springer Monographs in Mathematics (2003). {{ISBN|3-540-44085-2}} {{ZBL|1007.03002}}
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Latest revision as of 11:59, 23 November 2023

The assertion that every ideal in a Boolean algebra can be extended to a prime ideal. It is a consequence of the Axiom of choice, but is known to be strictly weaker. It implies the Tikhonov theorem for Hausdorff spaces.

References

  • T. Jech, "Set theory. The third millennium edition, revised and expanded" Springer Monographs in Mathematics (2003). ISBN 3-540-44085-2 Zbl 1007.03002
How to Cite This Entry:
Prime ideal theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Prime_ideal_theorem&oldid=39383