Algebraic Lattice

An algebraic lattice $(L,\wedge <!--\; \wedge \; -->,\vee <!--\; \vee \; -->)$ is a set $L$ with two binary operations meet and join, $\wedge <!--\; \wedge \; -->$ and $\vee <!--\; \vee \; -->$ such that both operations are commutative and associative and the absorption law holds.

I.e. $\mathrm{\forall <!--\; \forall \; -->}a,b,c\in <!--\; \in \; -->L$

1. commutivity: $a\wedge <!--\; \wedge \; -->b=b\wedge <!--\; \wedge \; -->a$, $a\vee <!--\; \vee \; -->b=b\vee <!--\; \vee \; -->a$
2. associativity: $(a\wedge <!--\; \wedge \; -->b)\wedge <!--\; \wedge \; -->c=a\wedge <!--\; \wedge \; -->(b\wedge <!--\; \wedge \; -->c)$, $(a\vee <!--\; \vee \; -->b)\vee <!--\; \vee \; -->c=a\vee <!--\; \vee \; -->(b\vee <!--\; \vee \; -->c)$
3. absorption law: $a=a\wedge <!--\; \wedge \; -->(a\vee <!--\; \vee \; -->b)=a\vee <!--\; \vee \; -->(a\wedge <!--\; \wedge \; -->b)$