Kunze Linear Algebra · Problem 4.4.7

Polynomials

Mathematics — Methods · gcd-subfield-extension

Problem

Let KK be a subfield of a field FF, and suppose ff, gg are polynomials in K[x]K[x]. Let MKM_K be the ideal generated by ff and gg in K[x]K[x] and MFM_F be the ideal they generate in F[x]F[x]. Show that MKM_K and MFM_F have the same monic generator.

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