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- Kummer_ring abstract "In abstract algebra, a Kummer ring is a subring of the ring of complex numbers, such that each of its elements has the formwhere ζ is an mth root of unity, i.e.and n0 through nm−1 are integers.A Kummer ring is an extension of , the ring of integers, hence the symbol . Since the minimal polynomial of ζ is the mth cyclotomic polynomial, the ring is an extension of degree (where φ denotes Euler's totient function).An attempt to visualize a Kummer ring on an Argand diagram might yield something resembling a quaint Renaissance map with compass roses and rhumb lines.The set of units of a Kummer ring contains.By Dirichlet's unit theorem, there are also units of infinite order,except in the cases m = 1, m = 2 (in which case we have the ordinary ring of integers), the case m = 4 (the Gaussian integers) and the cases m = 3, m = 6 (the Eisenstein integers).Kummer rings are named after Ernst Kummer, who studied the unique factorization of their elements.".
- Kummer_ring wikiPageID "3279941".
- Kummer_ring wikiPageRevisionID "591762184".
- Kummer_ring hasPhotoCollection Kummer_ring.
- Kummer_ring subject Category:Cyclotomic_fields.
- Kummer_ring subject Category:Ring_theory.
- Kummer_ring type CyclotomicFields.
- Kummer_ring type Field108569998.
- Kummer_ring type GeographicalArea108574314.
- Kummer_ring type Location100027167.
- Kummer_ring type Object100002684.
- Kummer_ring type PhysicalEntity100001930.
- Kummer_ring type Region108630985.
- Kummer_ring type Tract108673395.
- Kummer_ring type YagoGeoEntity.
- Kummer_ring type YagoLegalActorGeo.
- Kummer_ring type YagoPermanentlyLocatedEntity.
- Kummer_ring comment "In abstract algebra, a Kummer ring is a subring of the ring of complex numbers, such that each of its elements has the formwhere ζ is an mth root of unity, i.e.and n0 through nm−1 are integers.A Kummer ring is an extension of , the ring of integers, hence the symbol .".
- Kummer_ring label "Anel de Kummer".
- Kummer_ring label "Anello di Kummer".
- Kummer_ring label "Kummer ring".
- Kummer_ring label "Кольцо Куммера".
- Kummer_ring label "حلقة كومر".
- Kummer_ring sameAs Anello_di_Kummer.
- Kummer_ring sameAs Anel_de_Kummer.
- Kummer_ring sameAs m.09305y.
- Kummer_ring sameAs Q2813419.
- Kummer_ring sameAs Q2813419.
- Kummer_ring sameAs Kummer_ring.
- Kummer_ring wasDerivedFrom Kummer_ring?oldid=591762184.
- Kummer_ring isPrimaryTopicOf Kummer_ring.