Proof that: (a) The relation given by a b a - b Z is

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Proof that:

(a) The relation given by a ∼ b ⇔ a - b ϵ Z is a congruence relation on the additive group Q.
(b) The set Q/Z of equivalence classes is an infinite abelian group.

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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 13, 2023 03:08 AM

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Proof that: (a) The relation given by a b a - b Z is

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a To prove that the relation given by a b a b Z is a congruence relation on the additive group Q we ...View the full answer

Algebra Graduate Texts In Mathematics 73

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