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Oct 18, 2023 at 9:36 comment added Z. M The ring map $\varphi$ in question is not an isomorphism when $n>1$. As you observed, the source ring has no $n$-th root of $z_1\dots z_n$, and that is an obstruction: the rational point $(1,\dots,1,2)$, say, has empty preimage under the map on rational points induced by $\varphi$.
Oct 17, 2023 at 19:20 history edited Yun Liu
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S Oct 17, 2023 at 18:25 review First questions
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