| 释义 |
- References
In algebra, an analytically normal ring is a local ring whose completion is a normal ring, in other words a domain that is integrally closed in its quotient field. {{harvtxt|Zariski|1950}} proved that if a local ring of an algebraic variety is normal, then it is analytically normal, which is in some sense a variation of Zariski's main theorem. {{harvs|txt|last=Nagata|year1=1958|year2=1962|loc2=Appendix A1, example 7}} gave an example of a normal Noetherian local ring that is analytically reducible and therefore not analytically normal. References - {{citation|mr=0097395|last=Nagata|first= Masayoshi|title=An example of a normal local ring which is analytically reducible|journal=Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math.|volume= 31|year= 1958|pages= 83–85|url= http://projecteuclid.org/euclid.kjm/1250776950}}
- {{citation|authorlink=Masayoshi Nagata|last=Nagata|first= Masayoshi|title=Local rings|series= Interscience Tracts in Pure and Applied Mathematics|volume= 13|publisher= Interscience Publishers|place=New York-London |year=1962|isbn= 978-0470628652}}
- {{citation| mr=0024158 |last=Zariski|first= Oscar|authorlink=Oscar Zariski|title=Analytical irreducibility of normal varieties|journal=Annals of Mathematics | series = Second Series |volume=49|year=1948|pages= 352–361|doi=10.2307/1969284}}
- {{citation|mr=0045413|last=Zariski|first= Oscar|title=Sur la normalité analytique des variétés normales|journal=Annales de l'Institut Fourier |volume=2 |year=1950|pages= 161–164|url=http://www.numdam.org/item?id=AIF_1950__2__161_0}}
- {{Citation | last1=Zariski | first1=Oscar | author1-link=Oscar Zariski | last2=Samuel | first2=Pierre | author2-link=Pierre Samuel | title=Commutative algebra. Vol. II | origyear=1960 | publisher=Springer-Verlag | location=Berlin, New York | isbn=978-0-387-90171-8 |mr=0389876 | year=1975}}
{{abstract-algebra-stub}} 1 : Commutative algebra |