Suppose that for every r E R, pqr 0. Show that R is isomorphic to R/I, × R/Iq.
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:Let R be a commutative ring with a multiplicative unit. Let p, q be distinct prime
integers. Define
I, := {r € R: pr = 0}
and
I, = {r € R: qr = 0}.
Suppose that for every r E R, pqr = 0. Show that R is isomorphic to
R/I, × R/Iq.
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