how to answer B (B) Suppose char F = 0. Then F contains a subring S such that SZ (i.e. there is anisomorphism f: S→ Z).Now, let T = {ab-¹ | a, b = S, b# 0} and define the map g : T → Q byg(ab-¹)=f(a)f(b)Show that g is an isomorphism so that T ≤ F is isomorphic to Q.

Given That : Isomorphism f :S→Z. T=ab-1 a, b∈S, b≠0 and define the mapping g:T→Q by gab-1=fafb.…

Answered: Suppose char F = 0.Then F contains a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 6E

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Suppose char F = 0.Then F contains a subring S such that SZ (i.e. there is an isomorphism f: S→ Z). Now, let T = {ab-¹ | a, b = S, b# 0} and define the map g: T→Q by g(ab-¹)= f(a) f(b) Show that g is an isomorphism so that T ≤ F is isomorphic to Q.