query: Definition of Euclidean domain
positive_passages.docid: 17161
positive_passages.text: Can anyone make me understand in simple language why the second condition for being an Euclidean domain is superfluous?
negative_passages.docid: 148804
negative_passages.text: Norm-Euclidean rings?
negative_passages.docid: 130073
negative_passages.text: $N(ab) \geq N(a)$ is not necessary for the ring to be euclidean
negative_passages.docid: 75764
negative_passages.text: Regularity of a domain - definition
negative_passages.docid: 7011
negative_passages.text: Integral domain with fraction field equal to $\mathbb{R}$
negative_passages.docid: 130278
negative_passages.text: Vector Applications in Euclidean Geometry
negative_passages.docid: 134539
negative_passages.text: Euclidean and induction with prime numbers
negative_passages.docid: 67699
negative_passages.text: Integral domain that is integrally closed, one-dimensional and not noetherian
negative_passages.docid: 33427
negative_passages.text: Why is Euclidean distance not a good metric in high dimensions?
negative_passages.docid: 27652
negative_passages.text: metric on the Euclidean Group
negative_passages.docid: 65785
negative_passages.text: Difference between Euclidean space and vector space?
negative_passages.docid: 664
negative_passages.text: Minkowski's complex Euclidean space vs. the real pseudo-Euclidean version
negative_passages.docid: 50605
negative_passages.text: Extended Euclidean algorithm
negative_passages.docid: 14158
negative_passages.text: Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
negative_passages.docid: 29014
negative_passages.text: Book recommendation on plane Euclidean geometry
negative_passages.docid: 73344
negative_passages.text: Definition of irreducible polynomial via the units of an integral domain.
negative_passages.docid: 24653
negative_passages.text: Integral in $n-$dimensional euclidean space