Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(d) Explain why the following "proof" is incorrect: "Claim: The integral domain R = {a+b√√2 | a, b = Z} is not a unique factorisation domain. Proof. In R we have the factorisations 2 = √√2. √2 and 2 (2+√2) (2 - √2). These are two different factorisations of the element 2 Є R, which shows that R is not a unique factorisation domain." (e) Is the element 7+ 5√2 a unit of the integral domain R = {a + b√√2 | a, b = Z}? Justify your answer.

(d) Explain why the following "proof" is incorrect: "Claim: The integral domain R = {a+b√√2 | a, b = Z} is not a unique factorisation domain. Proof. In R we have the factorisations 2 = √√2. √2 and 2 (2+√2) (2 - √2). These are two different factorisations of the element 2 Є R, which shows that R is not a unique factorisation domain." (e) Is the element 7+ 5√2 a unit of the integral domain R = {a + b√√2 | a, b = Z}? Justify your answer.

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
(d) Explain why the following "proof" is incorrect: "Claim: The integral domain R = {a+b√√2 | a, b = Z} is not a unique factorisation domain. Proof. In R we have the factorisations 2 = √√2. √2 and 2 (2+√2) (2 - √2). These are two different factorisations of the element 2 Є R, which shows that R is not a unique factorisation domain." (e) Is the element 7+ 5√2 a unit of the integral domain R = {a + b√√2 | a, b = Z}? Justify your answer.
Transcribed Image Text:(d) Explain why the following "proof" is incorrect: "Claim: The integral domain R = {a+b√√2 | a, b = Z} is not a unique factorisation domain. Proof. In R we have the factorisations 2 = √√2. √2 and 2 (2+√2) (2 - √2). These are two different factorisations of the element 2 Є R, which shows that R is not a unique factorisation domain." (e) Is the element 7+ 5√2 a unit of the integral domain R = {a + b√√2 | a, b = Z}? Justify your answer.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 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