In the ring of integers modulo 10, find the sub fields.
My attempt: $z_{10}$ is not a filed, since 10 is not a prime integer. So there are only trivial subfields. So {0,1} is the only subfield.
Is my approach and results correct.
2026-04-24 20:56:13.1777064173
sub fields of ring of integers modulo 10
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$\{0,1\}$ isn’t closed under addition though. Did you mean $\{0,5\}$?
Also, you missed $\{0,2,4,6,8\}$.
And if your definition requires subfield to share identity with $\mathbb Z_{10}$ I guess we have to back up and say there are no subfields (but that seems silly.)