# Prime ideal theorem

From Encyclopedia of Mathematics

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=54589