English

On the ubiquity of Arf rings

Commutative Algebra 2023-07-11 v2

Abstract

We introduce and develop the theory of weakly Arf rings, which is a generalization of Arf rings, initially defined by J. Lipman in 1971. We provide characterizations of weakly Arf rings and study the relation between these rings, the Arf rings, and the strict closedness of rings. Furthermore, we give various examples of weakly Arf rings that come from idealizations, fiber products, determinantal rings, and invariant subrings.

Keywords

Cite

@article{arxiv.2006.01330,
  title  = {On the ubiquity of Arf rings},
  author = {Ela Celikbas and Olgur Celikbas and Cătălin Ciupercă and Naoki Endo and Shiro Goto and Ryotaro Isobe and Naoyuki Matsuoka},
  journal= {arXiv preprint arXiv:2006.01330},
  year   = {2023}
}

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57 pages