If S is a subring of a ring R, then S[a] is a subring of R[x]. Exercise 2.35.1 Prove this assertion! In particular, this shows that Q[x] is a subring of R[r], which in turn is a subring of C[r].
If S is a subring of a ring R, then S[a] is a subring of R[x]. Exercise 2.35.1 Prove this assertion! In particular, this shows that Q[x] is a subring of R[r], which in turn is a subring of C[r].
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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abstract algebra
![**Example 2.35**
If \( S \) is a subring of a ring \( R \), then \( S[x] \) is a subring of \( R[x] \).
**Exercise 2.35.1**
Prove this assertion!
In particular, this shows that \( \mathbb{Q}[x] \) is a subring of \( \mathbb{R}[x] \), which in turn is a subring of \( \mathbb{C}[x] \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d940ce8-cba2-4a95-af25-aae0739ca5aa%2F3436ed24-3767-47df-a5b1-00241befce01%2Fwbj5cvb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example 2.35**
If \( S \) is a subring of a ring \( R \), then \( S[x] \) is a subring of \( R[x] \).
**Exercise 2.35.1**
Prove this assertion!
In particular, this shows that \( \mathbb{Q}[x] \) is a subring of \( \mathbb{R}[x] \), which in turn is a subring of \( \mathbb{C}[x] \).
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