group theory - How to generate addition table for ring $mathbb Z_{15}$?

How do I generate an addition table for ring R such that

$R = \mathbb{Z}_{15}$

or generally speaking, how to generate an addition table for any polynomial ring R?

I tried following Inactive notation as mentioned here, but it is generating blank output.

I have tried evaluating the following snippet

   (plus = Table[Inactive[Plus][a, b] == mod[a + b, 15] {a, 15}, {b,15}]) // TableForm