center of a lattice
Let $L$ be a bounded lattice^{}. An element $a\in L$ is said to be central if $a$ is complemented (http://planetmath.org/ComplementedLattice) and neutral (http://planetmath.org/SpecialElementsInALattice). The center of $L$, denoted $\mathrm{Cen}(L)$, is the set of all central elements of $L$.
Remarks.

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$0$ and $1$ are central: they are complements^{} of one another, both distributive^{} and dually distributive, and satisfying the property
$$a\wedge b=a\wedge c\text{and}a\vee b=a\vee c\text{imply}b=c\text{for all}b,c\in L$$ where $a\in \{0,1\}$, and therefore neutral.

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$\mathrm{Cen}(L)$ is a sublattice of $L$.

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$\mathrm{Cen}(L)$ is a Boolean algebra^{}.
References
 1 G. Grätzer, General Lattice Theory, 2nd Edition, Birkhäuser (1998).
Title  center of a lattice 

Canonical name  CenterOfALattice 
Date of creation  20130322 17:31:50 
Last modified on  20130322 17:31:50 
Owner  CWoo (3771) 
Last modified by  CWoo (3771) 
Numerical id  5 
Author  CWoo (3771) 
Entry type  Definition 
Classification  msc 06B05 
Defines  central element 