22. Let R be a commutative ring and let A be an ideal of R. Show that VA = {xe R:x" e A for some positive integer n} is an ideal of R such that (i) AC VĀ (iii) If R has unity and VA = R, then A = R. (ii) WA = VA %3D %3D
22. Let R be a commutative ring and let A be an ideal of R. Show that VA = {xe R:x" e A for some positive integer n} is an ideal of R such that (i) AC VĀ (iii) If R has unity and VA = R, then A = R. (ii) WA = VA %3D %3D
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
(i) ACVA
(ii) VA = VA
(iii) If R has unity and VA = R, then A = R.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e528139-5ea2-4f41-bbe0-f14973d6ee19%2F220bff77-f5c3-4752-a52d-ba40a892eea6%2F1fep1yv_processed.jpeg&w=3840&q=75)
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
(i) ACVA
(ii) VA = VA
(iii) If R has unity and VA = R, then A = R.
%3D
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