Blyth attemps to prove the following universal propety of a exterior algebra $\bigoplus_{n \geq 0} \bigwedge^n M$ of an $R$-module $M$. Let $l_M\colon M\to\bigoplus_{n \geq 0} \bigwedge^n M$ be a canonical projection of a direct sum ($\bigwedge^1M = M$).
Given an associative unitary $R$-algebra $N$ and an $R$-linear map $g\colon M\to N$ such that $g(m)^2 = 0$ for all $m \in M$, for each $n \geq 1$, consider $g'_n\colon M^n\to N$ described by $(m_1,...,m_n) \mapsto g(m_1)... g(m_2)$. Blyth claims that since $g(m)^2 = 0$ for all $m \in M$, each $g'_n$ is $R$-multilinear and alternating.
However, I don't see how it is alternating. Since the property $g(m)^2 = 0$ is used, it seems to me that a (nonexistant) commutativity of $N$ is used.
It's rather $\bigwedge^0M=R$, and the inclusion of $M$ goes to the next summand, $\bigwedge^1 M=M$.
We have $$0=g(x+y)^2 =(g(x)+g(y))^2 =g(x)^2+g(x)g(y)+g(y)g(x)+g(y)^2 =g(x)g(y)+g(y)g(x)$$