Counting subrings of $\mathbb{Z}^n$ of non-zero co-rank
نویسندگان
1 Department of Mathematics, The City College of New York, New York, NY 10031.
2 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.
3 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.
doi
10.30504/jims.2020.238412.1020چکیده
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 $r$.
