5.Let R be a commutative ring and a any element in R. Define the annhilator of a to be the set ann(a) = {r ∈ R | ra = 0}(that is, the set of all elements that multiply ato zero). Prove that ann(a)is an ideal of R.

5.Let R be a commutative ring and a any element in R. Define the annhilator of a to be the set ann(a) = {r ∈ R | ra = 0}(that is, the set of all elements that multiply ato zero). Prove that ann(a)is an ideal of R.

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 24E: 24. If is a commutative ring and is a fixed element of prove that the setis an ideal of . (The set...

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#5.Let R be a commutative ring and a any element in R. Define the annhilator of a to be the set ann(a) = {r ∈ R | ra = 0}(that is, the set of all elements that multiply ato zero). Prove that ann(a)is an ideal of R.

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