In class we started studying the formal power series ring $A[[x]]$ of a ring $A$ and I've been all day trying to find how the zero divisors of this formal power series ring $A[[x]]$ should be, if $A$ is a commutative ring with unity.
I suspect the answer is similar to the case of the polynomial ring $A[x]$: We have that $f\in A[x]$ is a zero divisor if and only if there exists $c\in A$, $c\neq 0$ such as $cf = 0$.
However I haven't been able to prove if this works to $A[[x]]$ as well, since the demonstration in the case of $A[x]$ involves applying induction of the degree of the polynomial.
I could really use some help or lead with this, either with the demonstration or to tell me I'm wrong in my suspicions and how the zero divisors should actually be.
Thanks fo reading me so far, and have a nice day wherever you are!