TY - JOUR ID - 118868 TI - Counting subrings of $\mathbb{Z}^n$ of non-zero co-rank JO - Journal of the Iranian Mathematical Society JA - JIMS LA - en SN - AU - Chimni, S. AU - Chinta, G. AU - Takloo-Bighash, R. AD - Department of Mathematics, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S Morgan St (M/C 249), Chicago, IL 60607. AD - Department of Mathematics, The City College of New York, New York, NY 10031. Y1 - 2020 PY - 2020 VL - 1 IS - 2 SP - 163 EP - 172 KW - $mathbb{Z^n}$ KW - subrings KW - Stirling numbers of the second kind DO - 10.30504/jims.2020.238412.1020 N2 - 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 $r$. UR - https://jims.ims.ir/article_118868.html L1 - https://jims.ims.ir/article_118868_57f0145a78e287eccee85f1c2bbf2a9d.pdf ER -