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O que (quem) é quadratic extension - definição
PAIR OF A MATHEMATICAL FIELD AND ITS SUBFIELD
Subfield (mathematics); Quadratic extension; Purely transcendental; Extension field; Quadratic field extension; Degree (field theory); Subextension (field theory); Trivial extension; Intermediate field; Adjunction (field theory); Extension of a field; Finitely generated field extension; Purely transcendental extension; Field Extension; Finitely generated extension; Subextension; Cubic field extension; Cubic extension; Transcendental field extension; Adjoining (field theory)
Field extension
In mathematics, particularly in algebra, a field extension is a pair of fields E\subseteq F, such that the operations of E are those of F restricted to E. In this case, F is an extension field of E and E is a subfield of F.
Quadratic irrational number
MATHEMATICAL CONCEPT
Quadratic surd; Quadratic irrationality; Quadratic Irrational Number; Quadratic irrationalities; Quadratic irrational; Quadratic irrational numbers
In mathematics, a quadratic irrational number (also known as a quadratic irrational, a quadratic irrationality or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the rational numbers.Jörn Steuding, Diophantine Analysis, (2005), Chapman & Hall, p.
Quadratic reciprocity
THEOREM
Law of quadratic reciprocity; Quadratic reciprocity rule; Aureum Theorema; Law of Quadratic Reciprocity; Quadratic reciprocity law; Quadratic reciprocity theorem; Quadratic Reciprocity; Qr theorem
In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most standard statement is:
Wikipédia
Field extension
In mathematics, particularly in algebra, a field extension is a pair of fields such that the operations of K are those of L restricted to K. In this case, L is an extension field of K and K is a subfield of L. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers.
Field extensions are fundamental in algebraic number theory, and in the study of polynomial roots through Galois theory, and are widely used in algebraic geometry.
