Comments on: Prove the Ring Isomorphism $R[x,y]/(x) \cong R[y]$ https://yutsumura.com/prove-the-ring-isomorphism-rxyx-cong-ry/ Thu, 27 Jul 2017 00:22:00 +0000 hourly 1 https://wordpress.org/?v=5.3.6 By: Examples of Prime Ideals in Commutative Rings that are Not Maximal Ideals – Problems in Mathematics https://yutsumura.com/prove-the-ring-isomorphism-rxyx-cong-ry/#comment-1949 Thu, 27 Jul 2017 00:11:24 +0000 https://yutsumura.com/?p=3961#comment-1949 […] The third example is the ring of polynomials in two variables $R=Q[x, y]$ over $Q$ and the principal ideal $I=(x)$ generated by $x$. The quotient ring $Q[x,y]/(x)$ is isomorphic to $Q[y]$. (The proof of this isomorphism is given in the post Prove the Ring Isomorphism $R[x,y]/(x) cong R]y]$.) […]

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