What are addition and multiplication for integers? What are the identity elements?
We call the operation of forming integer sums integer addition. We call the operation of forming integer products integer multiplication.
It is easy to see the following.1
We denote the additive identity of $\Z $ by $0_{\Z }$ and the multiplicative identity by $1_{\Z }$. When it is clear from context, we call $0_{\Z }$ “zero” and we call $1_{\Z }$ “one”.