  In this note, we study the Cohen-Macaulayness of non-Noetherian rings. We
show that Hochster's celebrated theorem that a finitely generated normal
semigroup ring is Cohen-Macaulay does not extend to non-Noetherian rings. We
also show that for any valuation domain $V$ of finite Krull dimension, $V[x]$
is Cohen-Macaulay in the sense of Hamilton-Marley.
