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center of a lattice
Let $L$ be a bounded lattice. An element $a\in L$ is said to be central if $a$ is complemented and neutral. The center of $L$, denoted $\operatorname{Cen}(L)$, is the set of all central elements of $L$.
Remarks.

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

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

$\operatorname{Cen}(L)$ is a Boolean algebra.
References
 1 G. Grätzer, General Lattice Theory, 2nd Edition, Birkhäuser (1998).
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central element
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