In
mathematics, an element ''p'' of a
partial order
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary ...
(P, ≤) is a meet prime element when ''p'' is the principal element of a
principal
Principal may refer to:
Title or rank
* Principal (academia), the chief executive of a university
** Principal (education), the office holder/ or boss in any school
* Principal (civil service) or principal officer, the senior management level in ...
prime ideal. Equivalently, if ''P'' is a
lattice
Lattice may refer to:
Arts and design
* Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material
* Lattice (music), an organized grid model of pitch ratios
* Lattice (pastry), an ornam ...
, ''p'' ≠ ''top'', and for all ''a'', ''b'' in ''P'',
:''a''∧''b'' ≤ ''p'' implies ''a'' ≤ ''p'' or ''b'' ≤ ''p''.
See also
*
Join and meet
In mathematics, specifically order theory, the join of a subset S of a partially ordered set P is the supremum (least upper bound) of S, denoted \bigvee S, and similarly, the meet of S is the infimum (greatest lower bound), denoted \bigwedg ...
References
*.
Order theory
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