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

Stanislav Atanasov, Nathan Kaplan, Benjamin Krakoff +1

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 an…