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In mathematics, an Arf ring was defined by Lipman (1971) to be a 1-dimensional commutative semi-local Macaulay ring satisfying some extra conditions studied by Cahit Arf (1948).

References

Arf, Cahit (1948), "Une interprétation algébrique de la suite des ordres de multiplicité d'une branche algébrique", Proceedings of the London Mathematical Society, Second series 50: 256–287, doi:10.1112/plms/s2-50.4.256, ISSN 0024-6115, MR 0031785
Lipman, Joseph (1971), "Stable ideals and Arf rings", American Journal of Mathematics (The Johns Hopkins University Press) 93 (3): 649–685, doi:10.2307/2373463, ISSN 0002-9327, JSTOR 2373463, MR 0282969

Mathematics Encyclopedia