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finite extension (Definition)

Let $ K$ an extension field of $ F$. We say that $ K$ is a finite extension if $ [K:F]$ is finite. That is, $ K$ is a finite dimensional space over $ F$.

An important result on finite extensions establishes that any finite extension is also an algebraic extension.



"finite extension" is owned by drini. [ owner history (1) ]
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See Also: extension field, algebraic, existence of the minimal polynomial, algebraic extension, the field extension $\mathbb{R}/\mathbb{Q}$ is not finite, algebraic sum and product

Other names:  finite field extension
Keywords:  Galois Theory, Field

Attachments:
a finite extension of fields is an algebraic extension (Theorem) by alozano
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Cross-references: algebraic extension, finite dimensional, extension field
There are 32 references to this entry.

This is version 5 of finite extension, born on 2001-11-08, modified 2003-05-21.
Object id is 708, canonical name is FiniteExtension.
Accessed 5725 times total.

Classification:
AMS MSC12F05 (Field theory and polynomials :: Field extensions :: Algebraic extensions)

Pending Errata and Addenda
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