query: Describe the prime elements of the ring $\mathbb Z[\sqrt{-2}]$
positive_passages.docid: 154845
positive_passages.text: Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?
negative_passages.docid: 39642
negative_passages.text: Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
negative_passages.docid: 65637
negative_passages.text: Squares in Polynomial Quotient Ring $ (\mathbb{Z}/2)[x] /(x^{17} - 1) $
negative_passages.docid: 74318
negative_passages.text: Find the nilpotents in $\mathbb{Z}_3[x]/(x^2-1)$
negative_passages.docid: 14191
negative_passages.text: How many elements does the ring $ℤ[X]/(X^2-3,2X-4)$ have? Describe the structure of this ring.
negative_passages.docid: 94157
negative_passages.text: Normal Ring and Prime Ideal whose Square is Principal
negative_passages.docid: 4105
negative_passages.text: Irreducible but not prime in $\mathbb{Z}[\sqrt{-5}] $
negative_passages.docid: 112043
negative_passages.text: Show that the ideal $ (2, 1 + \sqrt{-7} ) $ in $ \mathbb{Z} [\sqrt{-7} ] $ is not principal
negative_passages.docid: 31933
negative_passages.text: $x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
negative_passages.docid: 21946
negative_passages.text: What do prime ideals in $k[x,y]$ look like?
negative_passages.docid: 30401
negative_passages.text: Determining the structure of the quotient ring $\mathbb{Z}[x]/(x^2+3,p)$
negative_passages.docid: 96071
negative_passages.text: How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
negative_passages.docid: 120181
negative_passages.text: The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
negative_passages.docid: 142212
negative_passages.text: Let $q$ be a prime congruent to 3 mod 4, prove the quotient ring $\mathbb{Z}[i]/(q)$ is a field with $q^2$ elements
negative_passages.docid: 111996
negative_passages.text: Maximal and Prime Ideal in Z
negative_passages.docid: 109199
negative_passages.text: Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
negative_passages.docid: 130686
negative_passages.text: How is $3\pi-10$ element of $[-\pi/2,\pi/2]$?