algebraic reciprocity

См. также в других словарях:

• Reciprocity — may refer to: Reciprocity (Canadian politics) Reciprocity (photography), the relationship between the intensity of the light and duration of the exposure that result in identical exposure Traffic violations reciprocity where non resident drivers… …   Wikipedia

• Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

• Reciprocity (mathematics) — In mathematics, reciprocity may mean:* Quadratic reciprocity, a fundamental result in number theory. Generalisations include: **cubic reciprocity **biquadratic reciprocity **higher reciprocity laws **Artin reciprocity **Weil reciprocity for… …   Wikipedia

• Algebraic number theory — In mathematics, algebraic number theory is a major branch of number theory which studies the algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number… …   Wikipedia

• Quadratic reciprocity — The law of quadratic reciprocity is a theorem from modular arithmetic, a branch of number theory, which shows a remarkable relationship between the solvability of certain quadratic equations modulo different prime moduli.Although it allows us to… …   Wikipedia

• Cubic reciprocity — is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x3 ≡ p (mod q) is solvable; the word reciprocity comes from the form of the main theorem, which states that …   Wikipedia

• Artin reciprocity law — The Artin reciprocity law, established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of the global class field theory.[1] The term reciprocity law refers to a long line of… …   Wikipedia

• Proofs of quadratic reciprocity — In the mathematical field of number theory, the law of quadratic reciprocity, like the Pythagorean theorem, has lent itself to an unusual number of proofs. Several hundred proofs of the law of quadratic reciprocity have been found.Proofs that are …   Wikipedia

• Weil reciprocity law — In mathematics, the Weil reciprocity law is a result of André Weil holding in the function field K ( C ) of an algebraic curve C over an algebraically closed field K . Given functions f and g in K ( C ), i.e. rational functions on C , then: f ((… …   Wikipedia

• List of algebraic number theory topics — This is a list of algebraic number theory topics. Contents 1 Basic topics 2 Important problems 3 General aspects 4 Class field theory …   Wikipedia

• List of algebraic geometry topics — This is a list of algebraic geometry topics, by Wikipedia page. Contents 1 Classical topics in projective geometry 2 Algebraic curves 3 Algebraic surfaces 4 …   Wikipedia