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LoginCourse Queries Syllabus Queries 3 years ago
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The idea is to consider the unique ring homomoprphism
Show this is surjective, and find that the kernel is the principal ideal generated by the minimal polynomial of 2–√ over Q.
This assumes a bit of knowledge. It can be reformulated in more elementary terms, though. Please advise in case.
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manpreet![Tuteehub forum best answer]()
Best Answer
3 years ago
I am reading a syllaref="https://forum.tuteehub.com/tag/b">bus aref="https://forum.tuteehub.com/tag/b">bout Discrete Mathematics. One of the proref="https://forum.tuteehub.com/tag/b">blems encouraged in the syllaref="https://forum.tuteehub.com/tag/b">bus to solve is the following.
Define R={a+ref="https://forum.tuteehub.com/tag/b">b2–√:a,ref="https://forum.tuteehub.com/tag/b">b∈Q}R={a+ref="https://forum.tuteehub.com/tag/b">b2:a,ref="https://forum.tuteehub.com/tag/b">b∈Q} Find ff so ff defines an isomorphism between R and Q[x]/(f)Q[x]/(f). Any ideas on how to tackle this problem?