cg. 2. Let a, b, c, f, and g be elements of a commutative ring R with a‡OR. Prove that if a divide both b and c, then a divides bf + (Note that in a commutative ring R where s and t are elements in R, then s divides t if there is an element b R such that t=s*b AND S0R.) Proof/

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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Question
2. Let a, b, c, f, and g be elements of a commutative ring R with
a‡ OR. Prove that if a divide both b and c, then a divides bf + cg.
(Note that in a commutative ring R where s and t are elements in
R, then s divides t if there is an element b = R such that t = s*b
AND SOR.)
Proof/
Transcribed Image Text:2. Let a, b, c, f, and g be elements of a commutative ring R with a‡ OR. Prove that if a divide both b and c, then a divides bf + cg. (Note that in a commutative ring R where s and t are elements in R, then s divides t if there is an element b = R such that t = s*b AND SOR.) Proof/
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