What are the elements of the modular ring mod 7? [closed]

Question

Are the elements of a modular ring simply the set of all the numbers from 1 to p−1?

in this case p−1 = 6 ?

I asked this on the math stack exchange https://math.stackexchange.com/q/3375667 and was told that 0 is included in the the ring. Is this treated differently in CS ?