Let A and B be abelian groups (a) For each m 0, AZ m A mA (b) Z m Zn Z c , where c (m,n) (c) Describe AB, when A and Bare finitely generated ...

ANSWER a We can define a map A Zm AmA by a n a nA This map is bilinear and so it induces a homomorph ...

Let A and B be abelian groups. (a) For each m > 0, AZ m A/mA.

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Let A and B be abelian groups.

(a) For each m > 0, A⊗Z_m≅ A/mA.

(b) Z_m ⊗Zn ≅ Z_c, where c = (m,n).

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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 03:04 AM

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Let A and B be abelian groups. (a) For each m > 0, AZ m A/mA.

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ANSWER a We can define a map A Zm AmA by a n a nA This map is bilinear and so it induces a homomorph...View the full answer

Algebra Graduate Texts In Mathematics 73

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