In the proof of Theorem 7.7.2 of Weibel's introduction to homological algebra there is an isomorphism involves which I cannot decode nor derive the isomorphism. Let $\mathfrak{g}$ be a Lie algebra over a ring $k$ which is free as a $k$-module with basis $\{e_{\alpha}\}$, and $A=k[e_1,e_2,\ldots]$ the polynomial ring with indeterminates $e_{\alpha}$. Then in the proof he writes the following equation which I cannot understand what does it mean $$A\otimes \wedge^*\mathfrak{g}=\wedge^*\left(\oplus Ae_{\alpha}\right)=K(\bf{x}).$$
My question are:
(i) What does the notation $Ae_{\alpha}$ means?
(ii) What does the superscript $^* $ stands for. Do we consider the whole space or just its degree wise component.
(iii) How can I have the first equality between the tensor product and the exterior algebra.
Any help will be appreciated.