View source for Arf ring

{{Short description|1-dimensional ring with special properties}}
In [[mathematics]], an '''Arf ring''' was defined by {{harvtxt|Lipman|1971}} to be a 1-[[Krull dimension|dimensional]] [[commutative ring|commutative]] [[semi-local ring|semi-local]] [[Cohen–Macaulay ring|Macaulay]] [[ring (mathematics)|ring]] satisfying some extra conditions studied by {{harvs|txt|last=Arf|first=Cahit|authorlink=Cahit Arf|year=1948}}.

==References==
*{{Citation | last1=Arf | first1=Cahit | title=Une interprétation algébrique de la suite des ordres de multiplicité d'une branche algébrique | doi=10.1112/plms/s2-50.4.256 | mr=0031785 | year=1948 | journal=Proceedings of the London Mathematical Society | series = Second series | issn=0024-6115 | volume=50 | pages=256–287}}
*{{Citation | last1=Lipman | first1=Joseph | title=Stable ideals and Arf rings | jstor=2373463 | mr=0282969 | year=1971 | journal=[[American Journal of Mathematics]] | issn=0002-9327 | volume=93 | pages=649–685 | doi=10.2307/2373463 | issue=3 | publisher=The Johns Hopkins University Press}}

[[Category:Commutative algebra]]
[[Category:Turkish inventions]]


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