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