Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Which of the following are ring (i): f: (2Z, +,-) → (Z, +,-), (ii): ƒ: (Z8, +,-) → (Z4, +,-), - 2x - 1 (mod 4). 4x (mod 6). (iii): f: (Z8, +,-) → (Z6, +,-), (iv): f: (Z2 x Z5, +,-) → (Z5, +,-), (x,y) →x+y (mod 5) homomorphisms? 3x.

Which of the following are ring (i): f: (2Z, +,-) → (Z, +,-), (ii): ƒ: (Z8, +,-) → (Z4, +,-), - 2x - 1 (mod 4). 4x (mod 6). (iii): f: (Z8, +,-) → (Z6, +,-), (iv): f: (Z2 x Z5, +,-) → (Z5, +,-), (x,y) →x+y (mod 5) homomorphisms? 3x.

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
See similar textbooks
icon
Related questions
Question
**Question:** Which of the following are ring homomorphisms? 1. \( f : (2\mathbb{Z}, +, \cdot) \to (\mathbb{Z}, +, \cdot), \, x \mapsto 3x \). 2. \( f : (\mathbb{Z}_8, +, \cdot) \to (\mathbb{Z}_4, +, \cdot), \, x \mapsto 2x - 1 \mod 4 \). 3. \( f : (\mathbb{Z}_8, +, \cdot) \to (\mathbb{Z}_6, +, \cdot), \, x \mapsto 4x \mod 6 \). 4. \( f : (\mathbb{Z}_2 \times \mathbb{Z}_5, +, \cdot) \to (\mathbb{Z}_5, +, \cdot), \, (x, y) \mapsto x + y \mod 5 \). **Options:** - A. (i), (ii) - B. (ii), (iv) - C. (iii), (iv) - D. All - E. None
Transcribed Image Text:**Question:** Which of the following are ring homomorphisms? 1. \( f : (2\mathbb{Z}, +, \cdot) \to (\mathbb{Z}, +, \cdot), \, x \mapsto 3x \). 2. \( f : (\mathbb{Z}_8, +, \cdot) \to (\mathbb{Z}_4, +, \cdot), \, x \mapsto 2x - 1 \mod 4 \). 3. \( f : (\mathbb{Z}_8, +, \cdot) \to (\mathbb{Z}_6, +, \cdot), \, x \mapsto 4x \mod 6 \). 4. \( f : (\mathbb{Z}_2 \times \mathbb{Z}_5, +, \cdot) \to (\mathbb{Z}_5, +, \cdot), \, (x, y) \mapsto x + y \mod 5 \). **Options:** - A. (i), (ii) - B. (ii), (iv) - C. (iii), (iv) - D. All - E. None
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
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,
SEE MORE TEXTBOOKS