Suppose that * is an associative and commutative binary operation on a set S. Show that H

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Suppose that * is an associative and commutative binary operation on a set S. Show that H = {a ∈ S| a* a = a} is closed under *· (The elements of H are idempotents of the binary operation *·)

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A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

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Question Posted: Dec 26, 2022 08:17 AM

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Suppose that * is an associative and commutative binary operation on a set S. Show that H

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Let a b H By definition of H we have a a a and b b b Usin...View the full answer

A First Course In Abstract Algebra

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