For finite groups, the Krull-Schmidt-Remak-Theorem holds, i.e. if $$ H_1 \times H_2 \times \ldots \times H_k \cong G_1 \times G_2 \times \ldots \times G_l $$ where the $H_i, G_i$ could not be further decomposed, then $k = l$ and there exists a reordering $\pi : \{1,\ldots,k\}\to \{1,\ldots,k\}$ such that $H_i \cong G_{\pi(i)}$.
Does the same hold for finite semigroups, or finite monoids?