Basis for exterior algebra (infinite dimensional)

Let $$\{e_i\}_{i\in I}$$ be a basis for V where $$I$$ is some totally ordered indexing set. Fix $$k\in \mathbb{Z}^{\geq 0}$$. Do we get an induced basis on $$\bigwedge^k V$$, where $$\{e_1\wedge...\wedge e_k|e_i\in \{e_i\}\}$$ where we use the ordering on $$I$$ to order lowest to highest from left to right.