g) A ring with Characteristic 7 h) An irreducible element in Z but reducible in Z[i]
g) A ring with Characteristic 7 h) An irreducible element in Z but reducible in Z[i]
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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please solve parts g and h
![Question 2: If possible; Find an Example for each of the following (
a) Two non-trivial idempotent elements in Z20 (0 &1 are not included)
b) An Ideal I in a finite commutative Ring R where R/I is a Field
c) A reducible polynomial of degree 2 in Z3[x] but irreducible in Z5[x]
d) Two non-zero nilpotent elements in Z₂ Z8 such that their sum is nilpotent
e) A prime ideal but not a maximal in a commutative ring with unity.
f) A ring with only one maximal ideal and of order greater than 100.
g) A ring with Characteristic 7
h) An irreducible element in Z but reducible in Z[i]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8d2d027-204d-466e-850d-579ecb98c79e%2Fa19083b8-4235-4c74-98b7-4651b1ea62aa%2Fycysiug_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2: If possible; Find an Example for each of the following (
a) Two non-trivial idempotent elements in Z20 (0 &1 are not included)
b) An Ideal I in a finite commutative Ring R where R/I is a Field
c) A reducible polynomial of degree 2 in Z3[x] but irreducible in Z5[x]
d) Two non-zero nilpotent elements in Z₂ Z8 such that their sum is nilpotent
e) A prime ideal but not a maximal in a commutative ring with unity.
f) A ring with only one maximal ideal and of order greater than 100.
g) A ring with Characteristic 7
h) An irreducible element in Z but reducible in Z[i]
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