Let F be a field and let φ : F → F be a ring isomorphism....

Let F be a field and let φ : F → F be a ring isomorphism. Define Fix φ to be Fix φ = {a ∈ F | φ(a) = a}. That is, Fix φ is the set of all elements of F that are fixed under φ. Prove that Fix φ is a field. (b) Define φ : C → C by φ(a + bi) = a − bi. Take for granted that φ is a ring isomorphism (we proved this in class at some point). Find Fix φ.

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Colby Messinger answered 2 years ago

Prove the following: (a) Let A be a ring and B be a field. Let f...

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2 Let F be a field and let R = F[x, y] be the ring of...

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Let F be a field, and recall the notion of the characteristic of a ring; the...

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Let F be a field and R = Mn(F) the ring of n×n matrices with entires...

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. Let φ : R → S be a ring homomorphism of R onto S. Prove...

. Let φ : R → S be a ring homomorphism of R onto S. Prove the following: J ⊂ S is an ideal of S if and only if φ ^−1 (J) is an ideal of R.

Let (F, <) be an ordered field, let S be a nonempty subset of F, let...

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Let F be a field and let φ : F → F be a ring isomorphism....

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