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algebraic extensions

algebraic extensions is the plural of algebraic extension.

Meaning of algebraic extension

Noun

algebraic extension (plural algebraic extensions)

  1. (field theory) A field extension L/K which is algebraic over K (i.e., is such that every element of L is a root of some (nonzero) polynomial with coefficients in K).
    • What we now have to prove is that: if an overring R#42; of R is such that R#42; is an integral domain, R#42; is integral over R and the quotient field #92;mathfrak#123;L#125;#42; of R#42; is a finite algebraic extension of #92;mathfrak#123;L#125;, then R#42; is a local ring and a finite R-module.1964, Shreeram Shankar Abhyankar, Local Analytic Geometry, Academic Press, page 200

Questions about algebraic extensions

What is algebraic extensions the plural of?
Algebraic extensions is the plural of algebraic extension.

Words near algebraic extensions in the dictionary

  1. algebraic data type
  2. algebraic data types
  3. algebraic equation
  4. algebraic equations
  5. algebraic extension
  6. algebraic extensions
  7. algebraic function
  8. algebraic functions
  9. algebraic fundamental group
  10. algebraic fundamental groups
  11. algebraic geometer

Source and license

Adapted from Wiktionary: algebraic extensions (page history and authors); algebraic extension (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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