Question 2.(a) Prove that the triple < 4Z, +, > is a commutative ring, but not an integral domain.1X(b) Prove or disprove: the commutative ring Zp, 0, 0 has no zero divisors for each primePEP.

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Answered: Question 2. (a) Prove that the triple…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.3: The Field Of Quotients Of An Integral Domain

Problem 8E

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Question 2. (a) Prove that the triple 4Z, +, -> is a commutative ring, but not an integral domain. 1 (b) Prove or disprove: the commutative ring Z₂.0.0 has no zero divisors for each prime PEP.