Word.ws English Dictionary

algebraic closures

algebraic closures is the plural of algebraic closure.

Meaning of algebraic closure

Noun

algebraic closure (plural algebraic closures)

  1. (field theory) A field G such that every polynomial over F splits completely over G (i.e., every element of G is a root of some polynomial over F and every root of every polynomial over F is an element of G).
    • The calculation of these various Galois groups leads to a determination of the algebraic closures of the ground fields in the splitting fields of the corresponding vectorial polynomials.1999, Shreeram S. Abhyankar, “Galois Theory of Semilinear Transformations”, in Helmut Voelklein, David Harbater, J. G. Thompson, Peter Müller, editors, Aspects of Galois Theory, Cambridge University...

Questions about algebraic closures

What is algebraic closures the plural of?
Algebraic closures is the plural of algebraic closure.

Words near algebraic closures in the dictionary

  1. algebra over a ring
  2. algebraic
  3. algebraic analysis
  4. algebraic closure
  5. algebraic closure operator
  6. algebraic closures
  7. algebraic combinatorics
  8. algebraic curve
  9. algebraic curves
  10. algebraic data type
  11. algebraic data types

Source and license

Adapted from Wiktionary: algebraic closures (page history and authors); algebraic closure (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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