Let R be a commutative unital ring. Let I be an ideal of R. Denote by(I) the ideal in Rx] generated by the image of elements in I under thenatrual embedding incl : R → R[x]. Prove that R[r]/ (I) × (R/I)[x].

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Let R be a commutative unital ring. Let I be an ideal of R. Denote by (I) the ideal in R[a] generated by the image of elements in I under the natrual embedding incl : R → R[x]. Prove that R[a]/ (I) × (R/I)[x].

Let R be a commutative unital ring. Let I be an ideal of R. Denote by (I) the ideal in R[a] generated by the image of elements in I under the natrual embedding incl : R → R[x]. Prove that R[a]/ (I) × (R/I)[x].

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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Let R be a commutative unital ring. Let I be an ideal of R. Denote by
(I) the ideal in Rx] generated by the image of elements in I under the
natrual embedding incl : R → R[x]. Prove that R[r]/ (I) × (R/I)[x].

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