Let R be a ring. For a subset X C R, let (X) denote the ideal generated by X, i.e.,the smallest ideal of R that contains X. In class we showed that(X) ==XCIIis the intersection of all ideals of R that contain X.If X and Y are two subsets of R, prove that (XUY) = (X) + (Y).

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Answered: Let R be a ring. For a subset X C R,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Let R be a ring. For a subset X C R, let (X) denote the ideal generated by X, i.e., the smallest ideal of R that contains X. In class we showed that (X) = = XCI I is the intersection of all ideals of R that contain X. If X and Y are two subsets of R, prove that (XUY) = (X) + (Y).