I am reading Dummit and Foote on Ring Theory - ch 7

On page 228 D&F give examples of subrings

For example 2 they write

" is a sub-ring of as is for any integer n.

The ring is not a subring of for any "

My question is surely the ringa subring of if we identify the equivalence class with 0 and with 1is

Perhaps the point D&F are making is that 0 and 1 are not the same as and ?

Can someone help by clarifying this issue

Peter