How do I find and list the distinct principal ideals in $\mathbb{ℤ}_2\times\mathbb{ℤ}_3$?
I know that $\mathbb{ℤ}_2$ has $0,1$ and that $\mathbb{ℤ}_3$ has $0,1,2$, but I'm not sure how to list them and how to find ideals in $\mathbb{ℤ}_2\times\mathbb{ℤ}_3$.
Hint: First, find the six elements of $\Bbb Z_2\times\Bbb Z_3.$ Next, determine the principal ideals generated by each element. Some of them will generate the same principal ideal.