Notes on Algebraic Properties and Non-Standard Analysis of the Ring of Integers Modulo Infinitely Large Primes

@misc{mihara2026notes,
  title = {{Notes on Algebraic Properties and Non-Standard Analysis of the Ring of Integers Modulo Infinitely Large Primes}},
  author = {Tomoki Mihara},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.00512},
  eprint = {2605.00512},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.00512},
}

TY  - UNPB
TI  - Notes on Algebraic Properties and Non-Standard Analysis of the Ring of Integers Modulo Infinitely Large Primes
AU  - Tomoki Mihara
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2605.00512
UR  - https://arxiv.org/abs/2605.00512
AB  - As applications of non-standard analysis to the study of transcendence in the ring 𝒜 of integers modulo infinitely large primes, we extend transcendence criteria by Anzawa--Funakura and Matsusaka--Seki. Using the extension of the criterion by Anzawa--Funakura, we observe conditional relation between asymptotic behaviour of prime gaps and transcendence in 𝒜. We also summarise known algebraic and model theoretic results on 𝒜 for number theorists, and share topics in transcendental number theory with algebraists and model theorists.
ER  -