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Prime ideal theorem

From Encyclopedia of Mathematics
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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

  • 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=39384