query: Show that $A \cong \mathbb{C}^n$ with A a commutative algebra
positive_passages.docid: 17378
positive_passages.text: Characterize finite dimensional algebras without nilpotent elements
negative_passages.docid: 93031
negative_passages.text: How to show that $\mathbb{Z}$ with the operation $m*n=m+(-1)^m n$ is associative?
negative_passages.docid: 42883
negative_passages.text: Cross product in $\mathbb R^n$
negative_passages.docid: 141258
negative_passages.text: Why does $M \mathbin{\otimes_R} N \cong M_\mathfrak{p} \mathbin{\otimes_{R_\mathfrak{p}}} N$?
negative_passages.docid: 49166
negative_passages.text: $R^n \cong R^m$ iff $n=m$
negative_passages.docid: 38687
negative_passages.text: Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$
negative_passages.docid: 118299
negative_passages.text: Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
negative_passages.docid: 146047
negative_passages.text: Proving that $\cos(2\pi/n)$ is algebraic
negative_passages.docid: 92962
negative_passages.text: Rings with $a^5=a$ are commutative
negative_passages.docid: 115726
negative_passages.text: For $p,q$ prime and $p \neq q$ show that $C_p \times C_q \cong C_{pq}$
negative_passages.docid: 43645
negative_passages.text: Show that $G/H\cong S_3$
negative_passages.docid: 39895
negative_passages.text: Showing a free abelian group is generated by its basis
negative_passages.docid: 56097
negative_passages.text: If $A$ and $AB-BA$ commute, show that $AB-BA$ is nilpotent
negative_passages.docid: 158490
negative_passages.text: Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
negative_passages.docid: 35948
negative_passages.text: How to prove $D^n/S^{n-1}\cong S^n$?
negative_passages.docid: 8374
negative_passages.text: How to prove that $R/I \otimes_R M \cong M / IM$
negative_passages.docid: 78263
negative_passages.text: Prove $GL_n(\Bbb{R})/SL_n(\Bbb{R}) \cong \Bbb{R}^\times$