In the rings Z8 and Z6 find the units, zero divisors and nilpotent elements.
Recall that an element a in a ring is called nilpotent if an = 0R for some
positive integer n.
The units in are since . While are zero divisiors since and . The nilpotent elements can only be among the zero divisors. Let us check one element and you try the other two. We will check if is nilpotent: and this pattern repeats. Therefore, is not nipotent. Now test the other two.