(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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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 15, 2023 03:51 AM

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(a) Let G be the additive group of all polynomials in x with integer coefficients. Show that...

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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

Algebra Graduate Texts In Mathematics 73

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