Exercise 4, § 4

Let E be a vector space with an infinite basis over a field K of characteristic 2 ; let B be the exterior algebra $\Lambda E$ on this space, which is a commutative ring. Give an example of a formal power series $u \in B[[X]]$ such that $u^2 = 0$ but such that there exists no element $\gamma \neq 0$ of B for which $\gamma u = 0$.