(1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and only if the quotient ring R/I is a field. (i) prime ideal (ii) primary ideal (iii) Maximal ideal (2) Z/(5): (i) (5) (ii) 5Z (iii) {[0],[1],[2],[3],[4]} (3) If R is an integral domain has non zero characteristic, then Char(R)=.... (i) 5 (ii) 4 (iii)9 (4) Let K be integer ring module 12 and let I=([4]) and J=([6]) be ideals of K. Then [2] belong to (i)I+J (ii)I.J (iii) I.J+ I (5) If f(x) =........ then f(x) is reducible in Z5[x]. (i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x² + 2
(1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and only if the quotient ring R/I is a field. (i) prime ideal (ii) primary ideal (iii) Maximal ideal (2) Z/(5): (i) (5) (ii) 5Z (iii) {[0],[1],[2],[3],[4]} (3) If R is an integral domain has non zero characteristic, then Char(R)=.... (i) 5 (ii) 4 (iii)9 (4) Let K be integer ring module 12 and let I=([4]) and J=([6]) be ideals of K. Then [2] belong to (i)I+J (ii)I.J (iii) I.J+ I (5) If f(x) =........ then f(x) is reducible in Z5[x]. (i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x² + 2
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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Question
![(1) Let I be a proper ideal of the commutative ring R with identity. Then I
is a ........
if and only if the quotient ring R/I is a field.
(i) prime ideal (ii) primary ideal (iii) Maximal ideal
(2) Z/(5):
(i) (5)
(ii) 5Z (iii) {[0],[1],[2],[3],[4]}
(3) If R is an integral domain has non zero characteristic, then
Char(R)=.....
(i) 5 (ii) 4
(iii)9
(4) Let K be integer ring module 12 and let I=([4]) and J=([6]) be
ideals of K. Then [2] belong to
...
(i)I+J (ii)I.J (iii) I.J+ I
(5) If f(x)
then f(x) is reducible in Z5[x].
(i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x² + 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99aa0c96-e01d-4b42-aa18-6855a4836955%2Fc53a2ac1-4a6f-435d-be19-dea292e5bf7a%2Ftdu9069_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(1) Let I be a proper ideal of the commutative ring R with identity. Then I
is a ........
if and only if the quotient ring R/I is a field.
(i) prime ideal (ii) primary ideal (iii) Maximal ideal
(2) Z/(5):
(i) (5)
(ii) 5Z (iii) {[0],[1],[2],[3],[4]}
(3) If R is an integral domain has non zero characteristic, then
Char(R)=.....
(i) 5 (ii) 4
(iii)9
(4) Let K be integer ring module 12 and let I=([4]) and J=([6]) be
ideals of K. Then [2] belong to
...
(i)I+J (ii)I.J (iii) I.J+ I
(5) If f(x)
then f(x) is reducible in Z5[x].
(i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x² + 2
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