1) If $≤$ is a partial order on a set $A$, show that there is a total order $ <=^(**) $ on $A$ such that $a ≤ b => a <=^(**) b$. (Hint: Use Zorn’s lemma.)
2) If $L$ is a lattice we say that an element $a in L$ is join irreducible if $ a=b vv c $ implies $a = b$ or $a = c$. If $L$ is a finite lattice show that every element is of the form $a_1 vv ··· vv a_n$, where each $a_i$ is join irreducible.
Se conoscete la soluzione o come impostarla grazie in anticipo.