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- Fundamental_unit_(number_theory) abstract "In algebraic number theory, a fundamental unit is a generator (modulo the roots of unity) for the unit group of the ring of integers of a number field, when that group has rank 1 (i.e. when the unit group modulo its torsion subgroup is infinite cyclic). Dirichlet's unit theorem shows that the unit group has rank 1 exactly when the number field is a real quadratic field, a complex cubic field, or a totally imaginary quartic field. When the unit group has rank ≥ 1, a basis of it modulo its torsion is called a fundamental system of units. Some authors use the term fundamental unit to mean any element of a fundamental system of units, not restricting to the case of rank 1 (e.g. Neukirch 1999, p. 42).".
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- Fundamental_unit_(number_theory) wikiPageWikiLink Algebraic_integer.
- Fundamental_unit_(number_theory) wikiPageWikiLink Algebraic_number_field.
- Fundamental_unit_(number_theory) wikiPageWikiLink Algebraic_number_theory.
- Fundamental_unit_(number_theory) wikiPageWikiLink Annals_of_Mathematics.
- Fundamental_unit_(number_theory) wikiPageWikiLink Cambridge_University_Press.
- Fundamental_unit_(number_theory) wikiPageWikiLink Category:Algebraic_number_theory.
- Fundamental_unit_(number_theory) wikiPageWikiLink Class_group.
- Fundamental_unit_(number_theory) wikiPageWikiLink Complex_cubic_field.
- Fundamental_unit_(number_theory) wikiPageWikiLink Continued_fraction.
- Fundamental_unit_(number_theory) wikiPageWikiLink Cubic_field.
- Fundamental_unit_(number_theory) wikiPageWikiLink Cyclic_group.
- Fundamental_unit_(number_theory) wikiPageWikiLink Dirichlets_unit_theorem.
- Fundamental_unit_(number_theory) wikiPageWikiLink Discriminant_of_an_algebraic_number_field.
- Fundamental_unit_(number_theory) wikiPageWikiLink Ideal_class_group.
- Fundamental_unit_(number_theory) wikiPageWikiLink Infinite_cyclic.
- Fundamental_unit_(number_theory) wikiPageWikiLink Narrow_class_group.
- Fundamental_unit_(number_theory) wikiPageWikiLink Number_field.
- Fundamental_unit_(number_theory) wikiPageWikiLink Pells_equation.
- Fundamental_unit_(number_theory) wikiPageWikiLink Quadratic_field.
- Fundamental_unit_(number_theory) wikiPageWikiLink Quartic_field.
- Fundamental_unit_(number_theory) wikiPageWikiLink Rank_of_an_abelian_group.
- Fundamental_unit_(number_theory) wikiPageWikiLink Real_quadratic_field.
- Fundamental_unit_(number_theory) wikiPageWikiLink Root_of_unity.
- Fundamental_unit_(number_theory) wikiPageWikiLink Springer-Verlag.
- Fundamental_unit_(number_theory) wikiPageWikiLink Springer_Science+Business_Media.
- Fundamental_unit_(number_theory) wikiPageWikiLink Torsion_subgroup.
- Fundamental_unit_(number_theory) wikiPageWikiLink Totally_imaginary_number_field.
- Fundamental_unit_(number_theory) wikiPageWikiLink Unit_(ring_theory).
- Fundamental_unit_(number_theory) wikiPageWikiLink Unit_group.
- Fundamental_unit_(number_theory) wikiPageWikiLinkText "Fundamental unit".
- Fundamental_unit_(number_theory) wikiPageWikiLinkText "Fundamental units".
- Fundamental_unit_(number_theory) wikiPageWikiLinkText "fundamental unit".
- Fundamental_unit_(number_theory) wikiPageWikiLinkText "fundamental units".
- Fundamental_unit_(number_theory) hasPhotoCollection Fundamental_unit_(number_theory).
- Fundamental_unit_(number_theory) title "Fundamental Unit".
- Fundamental_unit_(number_theory) urlname "FundamentalUnit".
- Fundamental_unit_(number_theory) wikiPageUsesTemplate Template:Citation.
- Fundamental_unit_(number_theory) wikiPageUsesTemplate Template:Cite_book.
- Fundamental_unit_(number_theory) wikiPageUsesTemplate Template:Harvnb.
- Fundamental_unit_(number_theory) wikiPageUsesTemplate Template:Math.
- Fundamental_unit_(number_theory) wikiPageUsesTemplate Template:MathWorld.
- Fundamental_unit_(number_theory) wikiPageUsesTemplate Template:Neukirch_ANT.
- Fundamental_unit_(number_theory) wikiPageUsesTemplate Template:Reflist.
- Fundamental_unit_(number_theory) subject Category:Algebraic_number_theory.
- Fundamental_unit_(number_theory) hypernym Generator.
- Fundamental_unit_(number_theory) type Software.
- Fundamental_unit_(number_theory) comment "In algebraic number theory, a fundamental unit is a generator (modulo the roots of unity) for the unit group of the ring of integers of a number field, when that group has rank 1 (i.e. when the unit group modulo its torsion subgroup is infinite cyclic). Dirichlet's unit theorem shows that the unit group has rank 1 exactly when the number field is a real quadratic field, a complex cubic field, or a totally imaginary quartic field.".
- Fundamental_unit_(number_theory) label "Fundamental unit (number theory)".
- Fundamental_unit_(number_theory) sameAs m.0bbnbx.
- Fundamental_unit_(number_theory) sameAs Q5508977.
- Fundamental_unit_(number_theory) sameAs Q5508977.
- Fundamental_unit_(number_theory) wasDerivedFrom Fundamental_unit_(number_theory)?oldid=654798476.
- Fundamental_unit_(number_theory) isPrimaryTopicOf Fundamental_unit_(number_theory).