Suppose S is a subset of an field F that contains at least two elements and satisfies both of the following conditions: x ∈ S and y ∈ S imply x − y ∈ S , and x ∈ S and y ≠ 0 ∈ S imply x y − 1 ∈ S . Prove that S is a field. This S is called a subfield of F . [Type here][Type here]
Suppose S is a subset of an field F that contains at least two elements and satisfies both of the following conditions: x ∈ S and y ∈ S imply x − y ∈ S , and x ∈ S and y ≠ 0 ∈ S imply x y − 1 ∈ S . Prove that S is a field. This S is called a subfield of F . [Type here][Type here]
Solution Summary: The author explains that S is a subset of F that contains at least two elements and satisfies the following conditions.
Suppose
S
is a subset of an field
F
that contains at least two elements and satisfies both of the following conditions:
x
∈
S
and
y
∈
S
imply
x
−
y
∈
S
, and
x
∈
S
and
y
≠
0
∈
S
imply
x
y
−
1
∈
S
. Prove that
S
is a field. This
S
is called a subfield of
F
.
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