Difference between revisions of "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 | + | 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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| − | * T. Jech, "Set theory. The third millennium edition, revised and expanded" Springer Monographs in Mathematics (2003). ISBN 3-540-44085-2 {{ZBL|1007.03002}} | + | * 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
Prime ideal theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Prime_ideal_theorem&oldid=39383