query: If $R$ is a finite boolean then $R \cong \mathbb{Z_2} \oplus \dots \oplus \mathbb{Z_2}$
positive_passages.docid: 149753
positive_passages.text: The structure of a Noetherian ring in which every element is an idempotent.
negative_passages.docid: 16507
negative_passages.text: Is $\mathbb{Z}= \{\dots -3, -2, -1, 0 ,1 ,2 , 3, \dots \}$ countable?
negative_passages.docid: 140868
negative_passages.text: Axiomatization of $\mathbb{Z}$ via well-ordering of positives.
negative_passages.docid: 38549
negative_passages.text: $\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
negative_passages.docid: 36043
negative_passages.text: If $ab \equiv r \pmod{p}$, and $x^2 \equiv a \pmod{p}$ then $y^2 \equiv b \pmod{p}$ for which condition of $r$?
negative_passages.docid: 149519
negative_passages.text: Prove that a Boolean ring is a Bezout ring .
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: 35777
negative_passages.text: $\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
negative_passages.docid: 9794
negative_passages.text: Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime
negative_passages.docid: 36142
negative_passages.text: What is $\mathbb Z \oplus \mathbb Z / \langle (2,2) \rangle$ isomorphic to?
negative_passages.docid: 92211
negative_passages.text: When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
negative_passages.docid: 105363
negative_passages.text: $\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
negative_passages.docid: 136756
negative_passages.text: Computational check whether $G\cong \tilde G$
negative_passages.docid: 66313
negative_passages.text: $\mathbb{Z}[i]/(a+bi) \cong \mathbb{Z}_{a^2+b^2}$ if $(a,b)=1$
negative_passages.docid: 76048
negative_passages.text: Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$?
negative_passages.docid: 35626
negative_passages.text: Is $(\mathbb{R}^2, lexicographic) \cong (\mathbb{R}, discrete)\times (\mathbb{R}, usual)$?
negative_passages.docid: 60777
negative_passages.text: Prove $\, a_1 \Bbb Z \cap \dotsb \cap a_r \mathbb{Z} = {\rm lcm}(a_1, \ldots, a_r) \Bbb Z$