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If A, B, C are ideals of a ring R such that BCA, prove that An (B + C) = B+ (AnC) = (An B) + (AnC).

If A, B, C are ideals of a ring R such that BCA, prove that An (B + C) = B+ (AnC) = (An B) + (AnC).

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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If A, B, C are ideals of a ring R such that BCA, prove that An (B + C) =B+ (AnC) = (An B) + (An C).
Transcribed Image Text:If A, B, C are ideals of a ring R such that BCA, prove that An (B + C) =B+ (AnC) = (An B) + (An C).
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