query: Difference between $\mathbb{Z}/p\mathbb{Z}$ and $\mathbb{Z}_p$
positive_passages.docid: 16559
positive_passages.text: Difference between $\mathbb{Z}/n\mathbb{Z}$ and $\mathbb{Z}_n$
negative_passages.docid: 155745
negative_passages.text: Ideals of $\mathbb{Z}[X]$
negative_passages.docid: 15387
negative_passages.text: Order of $GL(n, \mathbb Z_p)$
negative_passages.docid: 109610
negative_passages.text: Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
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: 92211
negative_passages.text: When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
negative_passages.docid: 57691
negative_passages.text: calculate (find the type of isomorphism) of $\mathbb Z_p/p\mathbb Z_p$ where p is prime
negative_passages.docid: 51695
negative_passages.text: Finding all homomorphisms between $\mathbb{Z}/m\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 91935
negative_passages.text: If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
negative_passages.docid: 134922
negative_passages.text: Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$
negative_passages.docid: 92703
negative_passages.text: Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
negative_passages.docid: 79367
negative_passages.text: Understanding the difference between two theorems related to $|G\,:\,K|=|H\,:\,K|\cdot|G\,:\,H|$.
negative_passages.docid: 130159
negative_passages.text: Meaning of ring notation $\Bbb Z_{(p)}$ in commutative algebra [localization]
negative_passages.docid: 141961
negative_passages.text: What is the difference between [[ $a == z* ]] and [ $a == z* ]?
negative_passages.docid: 147871
negative_passages.text: How do the prime ideals of $\mathbb{Z}_{k}$ look like?
negative_passages.docid: 98901
negative_passages.text: What's wrong with this argument for finding Aut($\mathbb{Z_p} \times \mathbb{Z_p}$)?
negative_passages.docid: 145112
negative_passages.text: Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic