Commit 2022-08-09 19:12 77d020f7
View on Github →feat(number_theory/number_field.lean): generalise range_eq_roots
to relative extensions (#15903)
The statement of range_eq_roots
is generalised to relative extensions: Let A
be an algebraically closed field and let x ∈ K
, with K
a number field. For F
, subfield of K
, the images of x
by the F
-algebra morphisms from K
to A
are exactly the roots in A
of the minimal polynomial of x
over F
.
The original version over ℚ
is a direct consequence. Still, I kept the statement since I think it is useful.