Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
QUESTION 10 Consider a ring 7I/2]={a + b[/2]| a,bEZ} where addition and multiplication on ZI/2jis defined as follows: (a + b[/2]) + (c+ d[/2 ]) = (a + c) + (b+ d)[/2] (a + b[/2 ])(c+ d[ /2]) = (ac+2bd) + (ad+ bc)[/2] Prove or disprove that (a) Z[/2] is a commutative ring. (b) Z[/2] is a ring with unity. (c) Z[/2] is a field.

QUESTION 10 Consider a ring 7I/2]={a + b[/2]| a,bEZ} where addition and multiplication on ZI/2jis defined as follows: (a + b[/2]) + (c+ d[/2 ]) = (a + c) + (b+ d)[/2] (a + b[/2 ])(c+ d[ /2]) = (ac+2bd) + (ad+ bc)[/2] Prove or disprove that (a) Z[/2] is a commutative ring. (b) Z[/2] is a ring with unity. (c) Z[/2] is a field.

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 10 Consider a ring 7I/2]={a + b[/2]| a,bEZ} where addition and multiplication on ZI/2jis defined as follows: (a + b[/2]) + (c+ d[/2 ]) = (a + c) + (b+ d)[/2] (a + b[/2 ])(c+ d[ /2]) = (ac+2bd) + (ad+ bc)[/2] Prove or disprove that (a) Z[/2] is a commutative ring. (b) Z[/2] is a ring with unity. (c) Z[/2] is a field.
Transcribed Image Text:QUESTION 10 Consider a ring 7I/2]={a + b[/2]| a,bEZ} where addition and multiplication on ZI/2jis defined as follows: (a + b[/2]) + (c+ d[/2 ]) = (a + c) + (b+ d)[/2] (a + b[/2 ])(c+ d[ /2]) = (ac+2bd) + (ad+ bc)[/2] Prove or disprove that (a) Z[/2] is a commutative ring. (b) Z[/2] is a ring with unity. (c) Z[/2] is a field.
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Ring
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
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