query: Finding all units in the ring $\Bbb Z_{5} \times \Bbb Z_{8}$
positive_passages.docid: 24203
positive_passages.text: Finding Zero Divisors and Units of Rings $\mathbb{Z}_n \times \mathbb{Z}_m$
negative_passages.docid: 21840
negative_passages.text: Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$
negative_passages.docid: 137201
negative_passages.text: Classifying $\mathbb{Z} \times \mathbb{Z} \times \mathbb{Z} / \langle(3,3,3)\rangle$
negative_passages.docid: 127814
negative_passages.text: Number of elements in the quotient ring $\mathbb{Z}_6 [x]/\langle 2x +4\rangle$
negative_passages.docid: 147968
negative_passages.text: Calculate the Factor Group $(\mathbb{Z}_4 \times \mathbb{Z}_6)/\langle(0,2)\rangle$
negative_passages.docid: 47522
negative_passages.text: group generators of $(\mathbb Z_{17}-\{0\},\times)$
negative_passages.docid: 98284
negative_passages.text: show $\Bbb Z_6 \cong \Bbb Z_3 \times \Bbb Z_2 $.
negative_passages.docid: 138383
negative_passages.text: group of units in a topological ring
negative_passages.docid: 1425
negative_passages.text: The Chinese Remainder Theorem for Rings.
negative_passages.docid: 156909
negative_passages.text: $\Bbb{Z}_{26} \rtimes_{\alpha} \Bbb{Z}_{5} \cong \Bbb{Z}_{26} \times \Bbb{Z}_{5}$ as groups.
negative_passages.docid: 92822
negative_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 102938
negative_passages.text: $\Bbb F_2[X]$ modules with 8 elements
negative_passages.docid: 5223
negative_passages.text: $\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$
negative_passages.docid: 35691
negative_passages.text: $\mathbb Z[\sqrt 3]$ contains infinitely many units
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: 127237
negative_passages.text: Let $I = \{a +ib \in \Bbb Z[i] : a$ and $b$ are both multiple of $5\}$.
negative_passages.docid: 35777
negative_passages.text: $\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$