Let R be a commutative ring and let A be an ideal of R. Show that VA = {x e R:x" e A for some positive integer n} is an ideal of R such that (i) AS VĀ (iii) If R has unity and VA = R, then A = R. (ii) VWA = VA %3D

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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Let R be a commutative ring and let A be an ideal
of R. Show that
VA = {x€ R:x" e A for some positive integer n}
is an ideal of R such that
(i) As VA
(ii) VA = VA
こ,
(iii) If R has unity and VA = R, then A = R.
%3D
Transcribed Image Text:Let R be a commutative ring and let A be an ideal of R. Show that VA = {x€ R:x" e A for some positive integer n} is an ideal of R such that (i) As VA (ii) VA = VA こ, (iii) If R has unity and VA = R, then A = R. %3D
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