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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) ACVA (iii) If R has unity and VA = R, then A R. (ii) VA = VA

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) ACVA (iii) If R has unity and VA = R, then A R. (ii) VA = VA

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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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) VWA = 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) VWA = VA こ。 (iii) If R has unity and VA = R, then A = R. %3D
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