Q4: prove or disprove each of the followinga) Every group has one generator.b) Every group of order less than 6 is abelian.c) The product of an integral domain is also integral domain.d) In a commutative ring with identity, every maximal ideal is prime.

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Answered: Q4: prove or disprove each of the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 4E

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Q4: prove or disprove each of the following a) Every group has one generator. b) Every group of order less than 6 is abelian. c) The product of an integral domain is also integral domain. d) In a commutative ring with identity, every maximal ideal is prime.