let $\mathbb {R} $ be a commutative ring with unity $I_R $. Consider $s= \{nI_R |n \in \mathbb{Z}\}$. Show that $s$ is a subring of $\mathbb {R}$.what is the unity of $s$?
Sol : $0=0 I_R \in s$ let $a=n I_R $ , b = $ x I _R $ $a-b = I_R (n-x) \in s $ $ab =I_R ( n I_R x)\in $ R is sub ring
Is true to show s is subring ? But I do not how to find unity Thanks in advance