8. (a) Let R be an integral domain with the property that any strictly descending chain of ideals 11 212 213 2... is finite. Prove that R is a field.

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter2: Basic Linear Algebra
Section2.3: The Gauss-jordan Method For Solving Systems Of Linear Equations
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8. (a) Let R be an integral domain with the property that any strictly
descending chain of ideals
11 212 213 2...
is finite. Prove that R is a field.
Transcribed Image Text:8. (a) Let R be an integral domain with the property that any strictly descending chain of ideals 11 212 213 2... is finite. Prove that R is a field.
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