Editing Algebraic number theory (section)

===Artin===
[[Emil Artin]] established the [[Artin reciprocity law]] in a series of papers (1924; 1927; 1930). This law is a general theorem in number theory that forms a central part of global class field theory.<ref>{{citation |author-link=Helmut Hasse |first=Helmut |last=Hasse |chapter=History of Class Field Theory | editor-last=Cassels| editor-first=J. W. S.| editor-link=J. W. S. Cassels| editor2-last=Fröhlich| editor2-first=Albrecht| editor2-link=Albrecht Fröhlich| title=Algebraic number theory| orig-year=1967 |year=2010 |edition=2nd| place=London| publisher=9780950273426| mr=0215665 |pages=266–279}}</ref> The term "[[reciprocity law (mathematics)|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 [[Gotthold Eisenstein|Eisenstein]] and Kummer to Hilbert's product formula for the [[Hilbert symbol|norm symbol]]. Artin's result provided a partial solution to [[Hilbert's ninth problem]].