Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Krull–Akizuki_theorem> ?p ?o. }
Showing items 1 to 10 of
10
with 100 items per page.
- Krull–Akizuki_theorem abstract "In algebra, the Krull–Akizuki theorem states the following: let A be a one-dimensional reduced noetherian ring, K its total ring of fractions. If B is a subring of a finite extension L of K containing A and is not a field, then B is a one-dimensional noetherian ring. Furthermore, for every nonzero ideal I of B, is finite over A.Note that the theorem does not say that B is finite over A. The theorem does not extend to higher dimension. One important consequence of the theorem is that the integral closure of a Dedekind domain A in a finite extension of the field of fractions of A is again a Dedekind domain. This consequence does generalize to a higher dimension: the Mori–Nagata theorem states that the integral closure of a noetherian domain is a Krull domain.".
- Krull–Akizuki_theorem wikiPageID "35947857".
- Krull–Akizuki_theorem wikiPageRevisionID "588897477".
- Krull–Akizuki_theorem subject Category:Theorems_in_algebra.
- Krull–Akizuki_theorem comment "In algebra, the Krull–Akizuki theorem states the following: let A be a one-dimensional reduced noetherian ring, K its total ring of fractions. If B is a subring of a finite extension L of K containing A and is not a field, then B is a one-dimensional noetherian ring. Furthermore, for every nonzero ideal I of B, is finite over A.Note that the theorem does not say that B is finite over A. The theorem does not extend to higher dimension.".
- Krull–Akizuki_theorem label "Krull–Akizuki theorem".
- Krull–Akizuki_theorem sameAs Krull%E2%80%93Akizuki_theorem.
- Krull–Akizuki_theorem sameAs Q6439289.
- Krull–Akizuki_theorem sameAs Q6439289.
- Krull–Akizuki_theorem wasDerivedFrom Krull–Akizuki_theorem?oldid=588897477.