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Q2) Select the correct answer for the following: (10 Marks) (1) Let I be a proper ideal of the commutative ring R with identity. The 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) x² + 2x² + 2x + 1 (ii) x² +1 (iii) x² + 2

Q2) Select the correct answer for the following: (10 Marks) (1) Let I be a proper ideal of the commutative ring R with identity. The 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) x² + 2x² + 2x + 1 (ii) x² +1 (iii) x² + 2

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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Q2) Select the correct answer for the following: (10 Marks) (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 + 2 x² + 2x + 1 (ii) x² +1 (iii) x² + 2
Transcribed Image Text:Q2) Select the correct answer for the following: (10 Marks) (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 + 2 x² + 2x + 1 (ii) x² +1 (iii) x² + 2
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