  We characterize well-founded algebraic lattices by means of forbidden
subsemilattices of the join-semilattice made of their compact elements. More
specifically, we show that an algebraic lattice $L$ is well-founded if and only
if $K(L)$, the join-semilattice of compact elements of $L$, is well-founded and
contains neither $[\omega]^{<\omega}$, nor $\underline\Omega(\omega^*)$ as a
join-subsemilattice. As an immediate corollary, we get that an algebraic
modular lattice $L$ is well-founded if and only if $K(L)$ is well-founded and
contains no infinite independent set. If $K(L)$ is a join-subsemilattice of
$I_{<\omega}(Q)$, the set of finitely generated initial segments of a
well-founded poset $Q$, then $L$ is well-founded if and only if $K(L)$ is
well-quasi-ordered.
