See algebraic closure in All languages combined, or Wiktionary
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"ref": "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 Press, page 1:",
"text": "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.",
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"ref": "2000, Alain M. Robert, A Course in p-adic Analysis, Springer, page 127:",
"text": "It turns out that the algebraic closure #x5C;mathbf#x7B;Q#x7D;#x5C;mathrm#x7B;a#x7D;#x5F;p is not complete, so we shall consider its completion #x5C;mathbf#x7B;C#x7D;#x5F;p: This field turns out to be algebraically closed and is a natural domain for the study of \"analytic functions.\"",
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"ref": "2004, John Swallow, Exploratory Galois Theory, Cambridge University Press, page 179:",
"text": "While #x5C;Complex contains an algebraic closure of #x5C;mathbb#x7B;Q#x7D;, it is by no means the only algebraically closed field containing an algebraic closure of #x5C;mathbb#x7B;Q#x7D;. We denote by #x5C;mathbb#x7B;Q#x7D;#x5C;mathrm#x7B;alg#x7D; the algebraic closure of #x5C;mathbb#x7B;Q#x7D; in #x5C;Complex; this field is simply the subfield of #x5C;Complex consisting of algebraic numbers. The field #x5C;mathbb#x7B;Q#x7D;#x5C;mathrm#x7B;alg#x7D; is isomorphic, then, to any algebraic closure of #x5C;mathbb#x7B;Q#x7D;, but even knowing that it is unique up to isomorphism very likely leaves us no more familiar with #x5C;mathbb#x7B;Q#x7D;#x5C;mathrm#x7B;alg#x7D; than we were.",
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"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)."
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"(algebra, field theory, of a field F) 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)."
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"text": "While #x5C;Complex contains an algebraic closure of #x5C;mathbb#x7B;Q#x7D;, it is by no means the only algebraically closed field containing an algebraic closure of #x5C;mathbb#x7B;Q#x7D;. We denote by #x5C;mathbb#x7B;Q#x7D;#x5C;mathrm#x7B;alg#x7D; the algebraic closure of #x5C;mathbb#x7B;Q#x7D; in #x5C;Complex; this field is simply the subfield of #x5C;Complex consisting of algebraic numbers. The field #x5C;mathbb#x7B;Q#x7D;#x5C;mathrm#x7B;alg#x7D; is isomorphic, then, to any algebraic closure of #x5C;mathbb#x7B;Q#x7D;, but even knowing that it is unique up to isomorphism very likely leaves us no more familiar with #x5C;mathbb#x7B;Q#x7D;#x5C;mathrm#x7B;alg#x7D; than we were.",
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