# Prime (order theory)

In mathematics, an element *p* of a partial order (P, ≤) is a **meet prime** element when *p* is the principal element of a principal prime ideal. Equivalently, if *P* is a lattice, *p* ≠ *top*, and for all *a*, *b* in *P*,

*a*∧*b*≤*p*implies*a*≤*p*or*b*≤*p*.

## See also

## References

- Roman, Steven (2008),
*Lattices and ordered sets*, New York: Springer, p. 50, ISBN 978-0-387-78900-2, MR 2446182.

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