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Extension (Algebra) should be merged into the main topic Algebraic extension. I know that an extension and an algebraic extension are different things, but it would help those reading algebraic extension, if they knew what an extension was first, and simply linking it at the end of the
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The article states: "Q and Q are fields but Ο and e are transcendental over Q." But Q and Q are isomorphic to the ring of polynomials Q, hence they are not fields.
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The term "sub K-algebra" seems stilted and clumsy to me - is "K-sub-algebra" bad? It sounds more natural.
176:"If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is a field."
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Knowledge. If you would like to participate, please visit the project page, where you can join
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Extension_(Algebra) is more of a "Would you like to know more?" than a "See also." IMHO.
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is the minimal polynomial for a over K (we can safely assume that it's monic). Then
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632:{\displaystyle a(a^{n-1}+b_{n-1}a^{n-2}+\ldots +b_{1})(-b_{0})^{-1}=1}
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Is this actually a field? What's the multiplicative inverse of a?
471:{\displaystyle a(a^{n-1}+b_{n-1}a^{n-2}+\ldots +b_{1})=-b_{0}}
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