Uniquely Euclidean norm: Difference between revisions
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{{Euclidean norm property}} | {{Euclidean norm property}} | ||
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==Definition== | ==Definition== | ||
A [[Euclidean norm]] on a [[commutative unital ring]] is termed '''uniquely Euclidean''' if it satisfies the following: for any two elements in the ring, there is only one possibility for the corresponding remainder (there may be multiple possibilities for the quotient, if the ring is not an [[integral domain]]). | A [[Euclidean norm]] on a [[commutative unital ring]] is termed '''uniquely Euclidean''' if it satisfies the following: for any two elements in the ring, there is only one possibility for the corresponding remainder (there may be multiple possibilities for the quotient, if the ring is not an [[integral domain]]). | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Filtrative Euclidean norm]] | |||
Latest revision as of 16:35, 12 May 2008
This article defines a property that can be evaluated for a Euclidean norm on a commutative unital ring
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Definition
A Euclidean norm on a commutative unital ring is termed uniquely Euclidean if it satisfies the following: for any two elements in the ring, there is only one possibility for the corresponding remainder (there may be multiple possibilities for the quotient, if the ring is not an integral domain).