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]
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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