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B All Ⓒ (i), (iii) D None E (i), (ii), (iv) (ii), (iii) Which of the following are true ? (i): R= {a+b√3|a, b € Z}. Then (R, +,-) is an integral domain. (ii): R= {a+b√ a, b e Z}. Then (R, +,) is an integral domain. (iii): R = {a+b√3 | a, b = Q}. Then (R, +,-) is a field. (iv): R= {a+b√3|a, b € Z}. Then (R, +,-) is a field. ...

B All Ⓒ (i), (iii) D None E (i), (ii), (iv) (ii), (iii) Which of the following are true ? (i): R= {a+b√3|a, b € Z}. Then (R, +,-) is an integral domain. (ii): R= {a+b√ a, b e Z}. Then (R, +,) is an integral domain. (iii): R = {a+b√3 | a, b = Q}. Then (R, +,-) is a field. (iv): R= {a+b√3|a, b € Z}. Then (R, +,-) 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
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B All Ⓒ (i), (iii) D None E (i), (ii), (iv) (ii), (iii) Which of the following are true ? (i): R= {a+b√3|a, b € Z}. Then (R, +,-) is an integral domain. (ii): R= {a+b√ a, b e Z}. Then (R, +,) is an integral domain. (iii): R = {a+b√3 | a, b = Q}. Then (R, +,-) is a field. (iv): R= {a+b√3|a, b € Z}. Then (R, +,-) is a field. ....
Transcribed Image Text:B All Ⓒ (i), (iii) D None E (i), (ii), (iv) (ii), (iii) Which of the following are true ? (i): R= {a+b√3|a, b € Z}. Then (R, +,-) is an integral domain. (ii): R= {a+b√ a, b e Z}. Then (R, +,) is an integral domain. (iii): R = {a+b√3 | a, b = Q}. Then (R, +,-) is a field. (iv): R= {a+b√3|a, b € Z}. Then (R, +,-) is a field. ....
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