(a) Let G be the additive group of all polynomials in x with integer coefficients. Show that...
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(a) Let G be the additive group of all polynomials in x with integer coefficients. Show that G is isomorphic to the group Q* of all positive rationaJs (under multiplication).
(b) The group Q* is free abelian with basis {p|p is prime in Z}.
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a To show that G is isomorphic to Q we need to construct a bijective group homomorphism between them Consider the map G Q defined by fx 2degf p1e1 pnen where degf is the degree of the polynomial f p1 ...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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