查看“︁狄利克雷单位定理”︁的源代码

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'''狄利克雷单位定理'''是[[代数数论]]两个基本定理之一，是由[[約翰·彼得·古斯塔夫·勒熱納·狄利克雷]]得出的。它指出在数域''O''<sub>''K''</sub>的代数整数环中单位群的可用一正实数[[regulator]]来度量，这正实数记为rank，可反映如何单位群在域''O''<sub>''K''</sub>的“稠密”程度。

==狄利克雷单位定理==
狄利克雷证明了单位群是有限生成的[[阿贝尔群]]，这乘法阿贝尔群阶等于:''r'' = ''r''<sub>1</sub> + ''r''<sub>2</sub> &minus; 1.数域 ''K'' 有扩张[''K'':'''Q''']=''r''=''r''<sub>1</sub>+2''r''<sub>2</sub>，<math>r_1</math>为''K''的[[实素点]]个数，<math>2r_2</math> 为''K''的[[复素点]]个数.

==参考文献==
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* {{Cite book| last=Cohen| first=Henri| title=A Course in Computational Algebraic Number Theory| publisher=Springer-Verlag| location=Berlin, New York| series=Graduate Texts in Mathematics| isbn=978-3-540-55640-4| mr=1228206| year=1993| volume=138| ref=harv| postscript=<!--None| unused_data=Henri Cohen-->
}}
*{{cite journal | last = Elstrodt | first = Jürgen | journal = Clay Mathematics Proceedings | title = The Life and Work of Gustav Lejeune Dirichlet (1805–1859) | work =  | publisher =  | year = 2007 | url = http://www.uni-math.gwdg.de/tschinkel/gauss-dirichlet/elstrodt-new.pdf | format = PDF | doi =  | accessdate = 2010-06-13 | ref = harv | archive-date = 2008-03-07 | archive-url = https://web.archive.org/web/20080307174514/http://www.uni-math.gwdg.de/tschinkel/gauss-dirichlet/elstrodt-new.pdf | dead-url = no }}
*[[Serge Lang]], ''Algebraic number theory'', ISBN 0-387-94225-4
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[[Category:代数]]
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