query: $\mathbb{Z}[\sqrt{11}]$ is norm-euclidean
positive_passages.docid: 153204
positive_passages.text: Euclidean domain $\mathbb{Z}[\sqrt{d}]$
negative_passages.docid: 109691
negative_passages.text: When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
negative_passages.docid: 512
negative_passages.text: Finding generator for the ideal generated by $a$ and $b$ in an euclidean domain
negative_passages.docid: 145390
negative_passages.text: Formal power series ring, norm.
negative_passages.docid: 47975
negative_passages.text: Closed cone in the euclidean space $\mathbb{R}^n$
negative_passages.docid: 26641
negative_passages.text: Problem about the definition of Euclidean domain
negative_passages.docid: 31295
negative_passages.text: $x+y\sqrt{2}$ infimum ($x,y\in \mathbb{Z}$)
negative_passages.docid: 77036
negative_passages.text: Normed vector spaces over finite fields
negative_passages.docid: 150572
negative_passages.text: Explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$
negative_passages.docid: 130073
negative_passages.text: $N(ab) \geq N(a)$ is not necessary for the ring to be euclidean
negative_passages.docid: 60665
negative_passages.text: Meaning of $\mathbb{Z}\left[\sqrt{3}\right]$?
negative_passages.docid: 6171
negative_passages.text: Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
negative_passages.docid: 72144
negative_passages.text: Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
negative_passages.docid: 77240
negative_passages.text: Show that $4 + \sqrt{10}$ is not prime in $\mathbb{Z}\bigl [\sqrt{10}\bigr]$
negative_passages.docid: 138459
negative_passages.text: Norm and Algebraic Integers
negative_passages.docid: 45911
negative_passages.text: Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer
negative_passages.docid: 97357
negative_passages.text: How many elements in a number field of a given norm?