Category:Euclidean Domains
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This category contains results about Euclidean Domains.
Definitions specific to this category can be found in Definitions/Euclidean Domains.
Let $\struct {D, +, \circ}$ be an integral domain.
Let there exist a Euclidean valuation on $D$.
Then $D$ is called a Euclidean domain.
Subcategories
This category has the following 3 subcategories, out of 3 total.
D
E
- Euclidean Valuations (empty)
Pages in category "Euclidean Domains"
The following 11 pages are in this category, out of 11 total.
E
- Element is Unit iff its Euclidean Valuation equals that of 1
- Euclid's Lemma for Euclidean Domains
- Euclid's Lemma for Irreducible Elements
- Euclid's Lemma for Irreducible Elements/General Result
- Euclidean Domain is GCD Domain
- Euclidean Domain is Principal Ideal Domain
- Euclidean Domain is UFD
- Euclidean Valuation of Non-Unit is less than that of Product