Exercise 36. Let A,B, and C be ideals of a commutative ring R. Prove the following: (1) A.(B.C) (A.B).C, (2) A.B B.A, (3) A.BCANB,
Exercise 36. Let A,B, and C be ideals of a commutative ring R. Prove the following: (1) A.(B.C) (A.B).C, (2) A.B B.A, (3) A.BCANB,
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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Transcribed Image Text:Exercise 36, Let A, B, and C be ideals of a commutative ring R. Prove the following:
(1) A.(B.C) (A.B).C, (2) A.B= B.A, (3) A.BCANB,
(4) A.(B+C) A.B+A.C, (5)AC B implies A.CC B.C, (6) A.(BnC) CA.BOA.C.
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