Counting Finite Index Subrings of $\mathbb{Z}^n$

Stanislav Atanasov; Nathan Kaplan; Benjamin Krakoff; Julia Menzel

doi:10.1007/978-3-030-37853-0_4

Counting Finite Index Subrings of $\mathbb{Z}^n$

Combinatorics 2022-01-25 v5 Number Theory

Authors: Stanislav Atanasov , Nathan Kaplan , Benjamin Krakoff , Julia Menzel

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We count subrings of small index of $\mathbb{Z}^n$ , where the addition and multiplication are defined componentwise. Let $f_n(k)$ denote the number of subrings of index $k$ . For any $n$ , we give a formula for this quantity for all integers $k$ that are not divisible by a 9th power of a prime, extending a result of Liu.

Keywords

subrings finite index $\mathbb{Z}^n$ counting number theory

Cite

@article{arxiv.1609.06433,
  title  = {Counting Finite Index Subrings of $\mathbb{Z}^n$},
  author = {Stanislav Atanasov and Nathan Kaplan and Benjamin Krakoff and Julia Menzel},
  journal= {arXiv preprint arXiv:1609.06433},
  year   = {2022}
}

Comments

29 pages. To appear in Acta Arithmetica

Counting Finite Index Subrings of $\mathbb{Z}^n$

Abstract

Keywords

Cite

Comments

Related papers