In each of the following cases we have a ring R and its subset SC R. Circle I if S is an ideal in R, Pr if it is prime, Pl if it is principal, M if it is maximal. It is possible that there are several correct answers, you have to circle all of them. You do not need to justify your answer. I Pr Pl M: R= Z, and S = 42. I Pr Pl M: R = Q, and S = 5Z. I Pr Pl M: R = Z, and S = N. I Pr Pl M: R = R[x], and S = {ƒ : ƒ(121) = 0}.
In each of the following cases we have a ring R and its subset SC R. Circle I if S is an ideal in R, Pr if it is prime, Pl if it is principal, M if it is maximal. It is possible that there are several correct answers, you have to circle all of them. You do not need to justify your answer. I Pr Pl M: R= Z, and S = 42. I Pr Pl M: R = Q, and S = 5Z. I Pr Pl M: R = Z, and S = N. I Pr Pl M: R = R[x], and S = {ƒ : ƒ(121) = 0}.
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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![In each of the following cases we have a ring R and its subset SC R. Circle I if
S is an ideal in R, Pr if it is prime, Pl if it is principal, M if it is maximal. It
is possible that there are several correct answers, you have to circle all of them.
You do not need to justify your answer.
I Pr Pl M: R = Z, and S = 42.
I
Pr Pl M: R = Q, and S
= 5Z.
I Pr Pl M: R = Z, and S = N.
I Pr Pl M: R = R[x], and S = {ƒ : ƒ(121) = 0}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F138da6ab-7efa-4b8c-b154-28405afcc8c9%2Ffc3418d2-f757-4308-bee2-faa5f4c648f6%2Fmnjajst_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In each of the following cases we have a ring R and its subset SC R. Circle I if
S is an ideal in R, Pr if it is prime, Pl if it is principal, M if it is maximal. It
is possible that there are several correct answers, you have to circle all of them.
You do not need to justify your answer.
I Pr Pl M: R = Z, and S = 42.
I
Pr Pl M: R = Q, and S
= 5Z.
I Pr Pl M: R = Z, and S = N.
I Pr Pl M: R = R[x], and S = {ƒ : ƒ(121) = 0}.
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