query: Properties of the quotient ring $\mathbb{Z}_6[x]/\langle2x+4\rangle$
positive_passages.docid: 27704
positive_passages.text: Cardinality of quotient ring $\mathbb{Z_6}[X]/(2X+4)$
negative_passages.docid: 124438
negative_passages.text: Find $|(\mathbb{Z} \oplus \mathbb{Z}) / \langle(3,6)\rangle|$ and determine if its cyclic
negative_passages.docid: 115876
negative_passages.text: $D_6 \cong D_3\times \mathbb Z_2$
negative_passages.docid: 91622
negative_passages.text: Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
negative_passages.docid: 62917
negative_passages.text: Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
negative_passages.docid: 93773
negative_passages.text: How many elements are in the quotient ring $\frac{\mathbb Z_3[x]}{\langle 2x^3+ x+1\rangle} $
negative_passages.docid: 33025
negative_passages.text: What is the order of $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ and is it cyclic?
negative_passages.docid: 73743
negative_passages.text: Number of elements in the quotient ring $\mathbb{Z}[X]/(X^2-3, 2X+4)$
negative_passages.docid: 30401
negative_passages.text: Determining the structure of the quotient ring $\mathbb{Z}[x]/(x^2+3,p)$
negative_passages.docid: 40975
negative_passages.text: Quotient of the ring of integers of a number field by a prime ideal
negative_passages.docid: 122312
negative_passages.text: How can I compute $\mathrm{Aut}(\mathbb{Z}/4\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z})$?
negative_passages.docid: 88199
negative_passages.text: The commutator subgroup of a quotient in terms of the commutator subgroup and the kernel
negative_passages.docid: 90433
negative_passages.text: Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$
negative_passages.docid: 41878
negative_passages.text: Cardinal of quotient rings of gaussian integers.
negative_passages.docid: 85752
negative_passages.text: Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
negative_passages.docid: 61709
negative_passages.text: Compute factor group $\dfrac{\mathbb{Z}_4 \times \mathbb{Z}_6}{\langle(2,3)\rangle}$ - Fraleigh p. 147 Example 15.11
negative_passages.docid: 3203
negative_passages.text: Quotient group $\mathbb Z^n/\ \text{im}(A)$