Is it possible to have ring isomorphisms between some subsets of size $s^k$ of Galois ring $\Bbb Z_2^{s^k}$ and the full Galois ring $\Bbb Z_s^k$?
2026-02-23 02:05:30.1771812330
On ring isomorphisms
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No, at least for $s\ne 2$, since this subset must be a subring of order/size s^k. In particular, it is an additive subgroup in the group $\Bbb Z_2^{s^k}(+)$. Hence $s^k$ must divide $2^{s^k}$.