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(a) R=Z, I = 35Z.

(a) R=Z, I = 35Z.

Advanced Engineering Mathematics
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 2:

 

For each of the following, you are given a ring R and an ideal I that is not maximal. Find an ideal M such that I C M C R (where each containment is proper). (a) R= Z, I = 35Z. (b) R= R[r], I = Hint: What is g(1)? {gh : h e R[x]}, where g = x³ – x² + 2x – 2. |
Transcribed Image Text:For each of the following, you are given a ring R and an ideal I that is not maximal. Find an ideal M such that I C M C R (where each containment is proper). (a) R= Z, I = 35Z. (b) R= R[r], I = Hint: What is g(1)? {gh : h e R[x]}, where g = x³ – x² + 2x – 2. |
(c) R= Z;[x], I = {gh : h e Z3[x]}, where g = Hint: What is g(1)? x3 + 4x? + 2x + 3. (d) R= C[x, y]= the ring of polynomials in the two variables complex coefficients, I x,y with {xh : h e C[x, y]}, Hint: The polynomial 2.x?y3+ixy²+x is in I. What is its constant term?
Transcribed Image Text:(c) R= Z;[x], I = {gh : h e Z3[x]}, where g = Hint: What is g(1)? x3 + 4x? + 2x + 3. (d) R= C[x, y]= the ring of polynomials in the two variables complex coefficients, I x,y with {xh : h e C[x, y]}, Hint: The polynomial 2.x?y3+ixy²+x is in I. What is its constant term?
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