Field theory MOC

Field extension

A field extension is the embedding of a field in a larger field , ring i.e. a Ring monomorphism or equivalently is a Subfield of . We write , and is thence called an extension field of . Then may be regarded as a vector space over , see Extension field as a unital associative algebra, and its dimension is called the degree of the extension, denoted .

A degree 2 extension is called a Quadratic extension, a degree 3 extension is called a Cubic extension, &c.

Types of extension

• Algebraic extension
  • Separable extension
• Simple extension
• Normal extension

See also

• Ring extension
• Adjunction field

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