18.1.2. Let R be a commutative ring with identity, and let a, b E R. Assume abis a unit in R. Do a and b have to be units?

To show this, let's consider a counterexample. Let R be the ring of integers Z, and let a = 2 and b…

Answered: 18.1.2. Let R be a commutative ring…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 35E: Let R be a commutative ring with unity whose only ideals are {0} and R Prove that R is a...

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18.1.2. Let R be a commutative ring with identity, and let a, b E R. Assume ab is a unit in R. Do a and b have to be units?