query: $\mathbb{Z}/n\mathbb{Z}$ is a semisimple ring provided n is square-free
positive_passages.docid: 152457
positive_passages.text: $\mathbb Z_n$ is semisimple iff $n$ is square free
negative_passages.docid: 30752
negative_passages.text: Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
negative_passages.docid: 19230
negative_passages.text: Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
negative_passages.docid: 142863
negative_passages.text: Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
negative_passages.docid: 127030
negative_passages.text: Simple example of non-arithmetic ring (non-distributive ideal lattice)
negative_passages.docid: 124864
negative_passages.text: A not free $\mathbb{Z}$-module
negative_passages.docid: 118073
negative_passages.text: Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?
negative_passages.docid: 12110
negative_passages.text: How are $2\mathbb{Z}\ncong3\mathbb{Z}$ different as rings?
negative_passages.docid: 76501
negative_passages.text: How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
negative_passages.docid: 142612
negative_passages.text: Matrix Ring of a Semisimple Ring
negative_passages.docid: 116943
negative_passages.text: Proof for maximal ideals in $\mathbb{Z}[x]$
negative_passages.docid: 104486
negative_passages.text: Ideal in $\mathbb Z[x]$ which is not two-generated
negative_passages.docid: 92583
negative_passages.text: Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
negative_passages.docid: 102072
negative_passages.text: Simple $M_n(D)$-module with $D$ a division ring
negative_passages.docid: 14003
negative_passages.text: $(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
negative_passages.docid: 93474
negative_passages.text: A Finite Boolean Ring is Generated by Finitely Many Copies of $\mathbb{Z} / 2 \mathbb{Z}$
negative_passages.docid: 17978
negative_passages.text: Isomorphism classes of $\mathbb{Z}[i]$ modules.