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22. 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) AC VĀ (iii) If R has unity and VA = R, then A = R. (ii) VWA = VA %3D

22. 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) AC VĀ (iii) If R has unity and VA = R, then A = R. (ii) VWA = VA %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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22. 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 (ii) VWA = VA (iii) If R has unity and VA = R, then A = R. (i) AS VA %3D
Transcribed Image Text:22. 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 (ii) VWA = VA (iii) If R has unity and VA = R, then A = R. (i) AS VA %3D
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