$R$ has no zero divisors . Let $a \in R$ , $0 \ne b \in R$ and $0 \ne n \in \mathbb Z$ be such that $na+ab=0$ , then is it true that $a=0$?

Question

Let $R$ be a commutative ring (not necessarily with unity) with no zero divisors . Let $a \in R$ , $0 \ne b \in R$ and $0 \ne n \in \mathbb Z$ be such that $na+ab=0$ , then is it true that $a=0$ ?

Answer 1

Take $R = \mathbb Z$, with $a=b=1$ and $n=-1$. Then $na+ab = -1+1=0$.