Answer to Question #175838 in Abstract Algebra for Barbie

Question

Find the zero divisors of R × Z₂ × Z₄

Answer 1

We remind that the zero divisor is an element $a\in X={\mathbb{R}}\times{\mathbb{Z}}_2\times{\mathbb{Z}}_4$ satisfying $ax=0$ with some nonzero $x\in X$. The only nonzero divisor of $\mathbb{R}$ is . $\mathbb{Z}_2$ and $\mathbb{Z}_4$ are the following groups: $\mathbb{Z}_2=\{0,1\}$ and $\mathbb{Z}_4=\{0,1,2,3\}$. For any nonzero $x$ from the groups there is $a$ satisfying: $a+x=0$ except 0. Thus, we receive the following zero divisors: $0\times(\mathbb{Z}_2\setminus\{0\})\times(\mathbb{Z}_4\setminus\{0\})$