Let $k[x]$ be a polynomial ring and $I$ an ideal (resp. graded). If $k\subset K$ is a field extension, then prove that there is a natural (resp. graded) isomorphism of $K$-algebras: $$K[x]/IK[x]\cong k[x]/I\otimes_{k}K.$$
2026-04-24 08:13:35.1777018415
Isomorphism of K-algebras
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