16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 4.4.7

Polynomials

Mathematics — Linear Algebra · gcd-independent-of-field

Problem

Let

K

be a subfield of a field

F

, and suppose

f

g

are polynomials in

K[x]

. Let

M_K

be the ideal generated by

f

and

g

K[x]

and

M_F

be the ideal they generate in

F[x]

. Show that

M_K

and

M_F

have the same monic generator.