This congruence is quoted from Matsumura, Commutative algebra. The explanation given for it is very brief and I believe I am missing some prerequisites to understand the proof.
(26.J, Page 189) Let $k$ be a ring, $A$ a $k$-algebra, $B=A[X_1,...,X_n]$. Then the module of Kähler differentials of $B$ over $k$, $\Omega_{B/k}$ can be decomposed as follows
$$\Omega_{B/k}\cong (\Omega_{A/k}\otimes _A B)\oplus BdX_1\otimes ....\otimes BdX_n$$
I know this is somehow derived from Theorem 57. Could someone please give an explanation or at least some references so that I can work it out on my own?
