Prime (order theory)

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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

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* Join and meet

## References

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

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