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} %3D is an ideal ofR such that (i) ASVA (iii) If R has unity and VA = R, then A = R. (ii) VA = VA %3D %3D

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} %3D is an ideal ofR such that (i) ASVA (iii) If R has unity and VA = R, then A = R. (ii) VA = VA %3D %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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Proof all do not copy at website available worng, only handwriting solution

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}
%3D
is an ideal of R such that
(i) AS VA
(iii) If R has unity and VA = R, then A = R.
(ii) VA = VA
%3D
%3D

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