@article {
author = {Chimni, S. and Chinta, G. and Takloo-Bighash, R.},
title = {Counting subrings of $\mathbb{Z}^n$ of non-zero co-rank},
journal = {Journal of the Iranian Mathematical Society},
volume = {1},
number = {2},
pages = {163-172},
year = {2020},
publisher = {Iranian Mathematical Society},
issn = {2717-1612},
eissn = {2717-1612},
doi = {10.30504/jims.2020.238412.1020},
abstract = {In this paper we study subrings of $\mathbb{Z^{n+k}}$ of co-rank $k$. We relate the number of such subrings $R$ with torsion subgroup $(\mathbb{Z^{n+k}}/R)_{\rm{tor}}$ of size $r$ to the number of full rank subrings of $\mathbb{Z^n}$ of index $r$.},
keywords = {$mathbb{Z^n}$,subrings,Stirling numbers of the second kind},
url = {https://jims.ims.ir/article_118868.html},
eprint = {https://jims.ims.ir/article_118868_57f0145a78e287eccee85f1c2bbf2a9d.pdf}
}