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# Basis and Finite and Infinite Field Extensions

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Find a basis for the extension of and also calculate
We know already that is infinite.
Give an example of fields and (with neither nor equal to ) such that:
a) and are both infinite
b) is infinite and is finite.

(See attached file for full problem description with proper symbols)

All gaps are Q, the rational numbers.

https://brainmass.com/math/finite-element-method/basis-finite-infinite-field-extensions-58988

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1. Find a basis of the extension of and also calculate
Let , then , ...

#### Solution Summary

Basis and Finite and Infinite Field Extensions are investigated. The solution is detailed and well presented.

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