2. Let a, b, c, f, and g be elements of a commutative ring R witha‡ 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 inR, then s divides t if there is an element b = R such that t = s*bAND SOR.)Proof/

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Answered: cg. 2. Let a, b, c, f, and g be…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 32E: 32. a. Let be an ideal of the commutative ring and . Prove that the setis an ideal of containing...

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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/