Can someone explain why there are no proper subrings of $\mathbb{Z}_{12}$? My explanation is that any proper subset of $\mathbb{Z}_{12}$ would have a different 0 element. Thus, it would not be a subring. I'm not sure how accurate this is, though.
Proper subring of $\mathbb{Z}_{12}$?
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abstract-algebra
ring-theory