How does the ring structure $10\mathbb{Z}/5\mathbb{Z}$

Question

Now the set of integers $10\mathbb{Z}=0,10,-10,20,-20,..$ and $5\mathbb{Z}=0,+5,-5,+10,-10,...$ .How does $10\mathbb{Z}/5\mathbb{Z}$ will look like -$10\mathbb{Z},5+10\mathbb{Z}$?

Answer 1

Quotient ring $\frac{I}{J} $ is possible iff J is an ideal of the ring I. Here in this case, $5\mathbb{Z} $ is not an ideal of $10\mathbb{Z} $ , even $5\mathbb{Z} $ is not a subring of $10\mathbb{Z} $.