Let $(X,\mathcal{B},μ)$ be a probability space and let $T_1,..., T_l$ be $l$ commuting invertible measure preserving transformations \linebreak of $X$. We show that if $T_1^{c_1} ... T_l^{c_l}$ is ergodic for each $(c_1,...,c_l)\neq (0,...,0)$, then the averages $\frac{1}{|\Phi_N|}∑_{u𝟄Φ_N}∏_{i=1}^r T_1^{p_{i1}(u)}... T_l^{p_{il}(u)}f_i$ converge in $L^2(μ)$ for all polynomials $p_{ij}\colon ℤ^d\toℤ$, all $f_i𝟄 L^{∞}(μ)$, and all F{ø}lner sequences $\{Φ_N\}_{N=1}^{∞}$ in $ℤ^d$.