Phrase guide

field extension

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

Any pair of fields, denoted L/K, such that K is a subfield of L.

Definition source: English Wiktionary via Wiktextract

Qualifier: field theory

Topics: algebra, algebraic-geometry, geometry, mathematics, sciences

Examples

  • 1998, David Goss, Basic Structures of Function Field Arithmetic, Springer, Corrected 2nd Printing, page 283, Note that the extension of L obtained by adjoining all division points of ψ includes at most a finite constant field extension.
  • 2007, Pierre Antoine Grillet, Abstract Algebra, Springer, 2bd Edition, page 530, A field extension of a field K is, in particular, a K-algebra. Hence any two field extensions of K have a tensor product that is a K-algebra.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

3 source translations are retained for this English entry.

  • Bulgarian: разширение (razširenie) — pair of fields such that one is a subfield of the other
  • Finnish: kuntalaajennus — pair of fields such that one is a subfield of the other
  • Polish: rozszerzenie ciała — pair of fields such that one is a subfield of the other