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 global class field theory. The term "reciprocity law" refers to a long line of more concrete number theoretic statements which it generalized, from the quadratic reciprocity law and the reciprocity laws of Eisenstein and Kummer to Hilbert's product formula for the norm symbol. Artin's result provided a partial solution to Hilbert's ninth problem.
Read more about Artin Reciprocity Law: Significance, Finite Extensions of Global Fields, Cohomological Interpretation, Alternative Statement
Famous quotes containing the words reciprocity and/or law:
“Between women love is contemplative; caresses are intended less to gain possession of the other than gradually to re-create the self through her; separateness is abolished, there is no struggle, no victory, no defeat; in exact reciprocity each is at once subject and object, sovereign and slave; duality become mutuality.”
—Simone De Beauvoir (1908–1986)
“And what other great nation has statutes and ordinances as just as this entire law that I am setting before you today? But take care and watch yourselves closely, so as neither to forget the things that your eyes have seen nor to let them slip from your mind all the days of your life; make them known to your children and your children’s children...”
—Bible: Hebrew, Deuteronomy 4:8,9.