An introduction to reciprocal complements of integral domains

Neil Epstein; Lorenzo Guerrieri

An introduction to reciprocal complements of integral domains

Commutative Algebra 2025-12-25 v1

Authors: Neil Epstein , Lorenzo Guerrieri

Abstract

Given an integral domain $D$ with fraction field $F$ , its *reciprocal complement* is the subring of $F$ generated by all $1/d$ for nonzero $d$ in $D$ . This paper serves doubly as a survey of the current state of the field and an update with new results and connections.

Keywords

integral domain fraction field reciprocal complement subring

Cite

@article{arxiv.2512.20801,
  title  = {An introduction to reciprocal complements of integral domains},
  author = {Neil Epstein and Lorenzo Guerrieri},
  journal= {arXiv preprint arXiv:2512.20801},
  year   = {2025}
}

Comments

19 pages. Comments welcome!

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