Question 2: 9 ma 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 Zs[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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

please solve parts d, e and f

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]
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,