query: Ideal for $2\times 2$ matrix entry in $\mathbb{Z}$
positive_passages.docid: 142863
positive_passages.text: Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
negative_passages.docid: 55900
negative_passages.text: Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
negative_passages.docid: 512
negative_passages.text: Finding generator for the ideal generated by $a$ and $b$ in an euclidean domain
negative_passages.docid: 17239
negative_passages.text: Find all ideals of ${\mathbb{Z}_n}$
negative_passages.docid: 67772
negative_passages.text: How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
negative_passages.docid: 45627
negative_passages.text: Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$
negative_passages.docid: 119052
negative_passages.text: Finding invertible elements in $\mathbb{Z}/m\mathbb{Z}$
negative_passages.docid: 108775
negative_passages.text: Identify the ring $\mathbb {Z}[i]/(2 + i) $
negative_passages.docid: 72640
negative_passages.text: $(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
negative_passages.docid: 148550
negative_passages.text: Units in quotient ring of $\mathbb Z[X]$
negative_passages.docid: 587
negative_passages.text: Ideal Generated by the Union of Two Ideals
negative_passages.docid: 87780
negative_passages.text: Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
negative_passages.docid: 122104
negative_passages.text: Ideal products and calculating with ideals
negative_passages.docid: 77903
negative_passages.text: Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$
negative_passages.docid: 19230
negative_passages.text: Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
negative_passages.docid: 102721
negative_passages.text: Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$
negative_passages.docid: 146243
negative_passages.text: Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$?