query: nZ is not ring isomorphism to mZ if n and m are 2 distinct positive integers
positive_passages.docid: 23879
positive_passages.text: If $m$ and $n$ are distinct positive integers, then $m\mathbb{Z}$ is not ring-isomorphic to $n\mathbb{Z}$
negative_passages.docid: 37904
negative_passages.text: Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
negative_passages.docid: 3778
negative_passages.text: If the matrix rings over two Rings of the same size are isomorphic, then the scalar rings are isomorphic
negative_passages.docid: 33455
negative_passages.text: Question on group homomorphisms involving the standard Z-basis
negative_passages.docid: 104562
negative_passages.text: Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
negative_passages.docid: 18540
negative_passages.text: Isomorphism from $\mathbb{C}[G]$ to $\prod_{i=1}^h M_{n_i}(\mathbb{C})$.
negative_passages.docid: 66169
negative_passages.text: Ring of order $n$ is isomorphic to $\Bbb Z/n\Bbb Z$, with $n$ square-free
negative_passages.docid: 61084
negative_passages.text: Examples of non-isomorphic fields with isomorphic group of units and additive group structure
negative_passages.docid: 155604
negative_passages.text: Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
negative_passages.docid: 18018
negative_passages.text: Proving that $4 \mid m - n$ is an equivalence relation on $\mathbb{Z}$
negative_passages.docid: 62635
negative_passages.text: Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
negative_passages.docid: 2884
negative_passages.text: $m,n>1$ are relatively prime integers , then are there at-least four idempotent (w.r.t. multiplication) elements in $\mathbb Z_{mn}$ ?
negative_passages.docid: 12110
negative_passages.text: How are $2\mathbb{Z}\ncong3\mathbb{Z}$ different as rings?
negative_passages.docid: 18343
negative_passages.text: Counting homomorphisms between $\Bbb Z$ and $\Bbb Z_n$ and also between $\Bbb Z_n$ and $\Bbb Q$
negative_passages.docid: 109596
negative_passages.text: Isomorphism from $\mathrm{Aut}(\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z})$ to $S_3$
negative_passages.docid: 135241
negative_passages.text: Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
negative_passages.docid: 55900
negative_passages.text: Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?