field extensionとは 意味・読み方・使い方

使用する際の注意点

• Related terminology:
  • ${\displaystyle L}$ may be said to be an extension field (または simply an extension) of ${\displaystyle K}$.
  • If a field ${\displaystyle F}$ exists which is a subfield of ${\displaystyle L}$ and of which ${\displaystyle K}$ is a subfield, then we may call ${\displaystyle F}$ an intermediate field (of ${\displaystyle L/K}$), or an intermediate extension or subextension (of ${\displaystyle K}$, または perhaps of ${\displaystyle L/K}$).
  • The field ${\displaystyle L}$ is a ${\displaystyle K}$-vector space. Its dimension is called the degree of the extension, denoted ${\displaystyle [L:K]}$.
  • The construction ${\displaystyle L/L}$ is called the trivial extension.
• Field extensions are fundamental in algebraic number theory and in the study of polynomial roots through Galois theory, and are widely used in algebraic geometry.

下位語

• algebraic extension
• transcendental extension
• simple extension
• trivial extension

Meronyms

• base field
• extension field

関連する語

• extension
• extension field

Further reading

• Field theory on Wikipedia.
• Glossary of field theory on Wikipedia.
• Tower of fields on Wikipedia.
• Primary extension on Wikipedia.
• Regular extension on Wikipedia.
• Extension Field on Wolfram MathWorld
• Extension of a field on Encyclopedia of Mathematics

アナグラム

• extension field