(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
(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
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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![(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 ...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99aa0c96-e01d-4b42-aa18-6855a4836955%2F73dc6d46-a5fb-4032-9aa6-18c34fed0a6a%2F5p6rz6l_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 ...
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