query: Is $\mathbf{Z}[x]/((x-n_1)\dots(x-n_m)) \cong \mathbf{Z}^m$
positive_passages.docid: 26749
positive_passages.text: $\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
negative_passages.docid: 1712
negative_passages.text: $ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
negative_passages.docid: 63478
negative_passages.text: Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
negative_passages.docid: 75970
negative_passages.text: $\mathbb Z[1/2]$ is not finitely generated?
negative_passages.docid: 102112
negative_passages.text: Idempotents in $\mathbb Z_n$
negative_passages.docid: 137422
negative_passages.text: $\mathrm{card}(\mathbb{Z}^n/M\mathbb{Z}^n) = |\det(M)|$?
negative_passages.docid: 98507
negative_passages.text: $\text{Aut}(F)$ is isomorphic to the multiplicative group of all $n\times n$ matrices over $\mathbb Z$
negative_passages.docid: 51898
negative_passages.text: Show that $\operatorname{Hom}_{R} (R,M) \cong M$
negative_passages.docid: 128711
negative_passages.text: $(\Bbb Z\oplus \Bbb Z)[X] \not\cong \Bbb Z[X]\oplus \Bbb Z[X]\,$?
negative_passages.docid: 83001
negative_passages.text: Easier way to show $(\mathbb{Z}/(n))[x]$ and $\mathbb{Z}[x] / (n)$ are isomorphic
negative_passages.docid: 33781
negative_passages.text: Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
negative_passages.docid: 118898
negative_passages.text: Is there a simple way of proving that $\text{GL}_n(R) \not\cong \text{GL}_m(R)$?
negative_passages.docid: 147564
negative_passages.text: Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?
negative_passages.docid: 22783
negative_passages.text: Is the set $Z_n = \{ 0, 1, . . . , n-1 \}$ for $n ≥ 1$ is a group under addition modulo n?
negative_passages.docid: 101164
negative_passages.text: Show that $B \cong \mathbb Z /2\mathbb Z$ for a Boolean field B
negative_passages.docid: 53266
negative_passages.text: Show that $R/I\otimes_R R/J\cong R/(I+J)$
negative_passages.docid: 19884
negative_passages.text: The units of $\mathbb Z_4[x]$