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- Algebraic_integer abstract "In number theory, an algebraic integer is a complex number that is a root of some monic polynomial (a polynomial whose leading coefficient is 1) with coefficients in ℤ (the set of integers). The set of all algebraic integers is closed under addition and multiplication and therefore is a subring of complex numbers denoted by A. The ring A is the integral closure of regular integers ℤ in complex numbers.The ring of integers of a number field K, denoted by OK, is the intersection of K and A: it can also be characterised as the maximal order of the field K.Each algebraic integer belongs to the ring of integers of some number field. A number x is an algebraic integer if and only if the ring ℤ[x] is finitely generated as an abelian group, which is to say, as a ℤ-module.".
- Algebraic_integer wikiPageID "98981".
- Algebraic_integer wikiPageLength "7866".
- Algebraic_integer wikiPageOutDegree "47".
- Algebraic_integer wikiPageRevisionID "677877219".
- Algebraic_integer wikiPageWikiLink Abelian_group.
- Algebraic_integer wikiPageWikiLink Abel–Ruffini_theorem.
- Algebraic_integer wikiPageWikiLink Algebraic_number_field.
- Algebraic_integer wikiPageWikiLink Bézout_domain.
- Algebraic_integer wikiPageWikiLink Category:Algebraic_numbers.
- Algebraic_integer wikiPageWikiLink Category:Integers.
- Algebraic_integer wikiPageWikiLink Coefficient.
- Algebraic_integer wikiPageWikiLink Complex_number.
- Algebraic_integer wikiPageWikiLink Constant_term.
- Algebraic_integer wikiPageWikiLink Cyclotomic_field.
- Algebraic_integer wikiPageWikiLink Degree_of_a_field_extension.
- Algebraic_integer wikiPageWikiLink Degree_of_a_polynomial.
- Algebraic_integer wikiPageWikiLink Dirichlets_unit_theorem.
- Algebraic_integer wikiPageWikiLink Eisenstein_integer.
- Algebraic_integer wikiPageWikiLink Finitely_generated_group.
- Algebraic_integer wikiPageWikiLink Free_abelian_group.
- Algebraic_integer wikiPageWikiLink Fundamental_unit_(number_theory).
- Algebraic_integer wikiPageWikiLink Gaussian_integer.
- Algebraic_integer wikiPageWikiLink Gausss_lemma_(polynomial).
- Algebraic_integer wikiPageWikiLink Greatest_common_divisor.
- Algebraic_integer wikiPageWikiLink If_and_only_if.
- Algebraic_integer wikiPageWikiLink Integer.
- Algebraic_integer wikiPageWikiLink Integral_element.
- Algebraic_integer wikiPageWikiLink Integrally_closed.
- Algebraic_integer wikiPageWikiLink Irreducible_polynomial.
- Algebraic_integer wikiPageWikiLink Monic_polynomial.
- Algebraic_integer wikiPageWikiLink Number_theory.
- Algebraic_integer wikiPageWikiLink Order_(ring_theory).
- Algebraic_integer wikiPageWikiLink Primitive_element_theorem.
- Algebraic_integer wikiPageWikiLink Principal_ideal_theorem.
- Algebraic_integer wikiPageWikiLink Quadratic_field.
- Algebraic_integer wikiPageWikiLink Quadratic_integer.
- Algebraic_integer wikiPageWikiLink Quintic_function.
- Algebraic_integer wikiPageWikiLink Rational_number.
- Algebraic_integer wikiPageWikiLink Resultant.
- Algebraic_integer wikiPageWikiLink Ring_of_integers.
- Algebraic_integer wikiPageWikiLink Root_of_unity.
- Algebraic_integer wikiPageWikiLink Square-free_integer.
- Algebraic_integer wikiPageWikiLink Square_number.
- Algebraic_integer wikiPageWikiLink Subring.
- Algebraic_integer wikiPageWikiLink Zero_of_a_function.
- Algebraic_integer wikiPageWikiLinkText "Algebraic integer".
- Algebraic_integer wikiPageWikiLinkText "algebraic integer".
- Algebraic_integer wikiPageWikiLinkText "ring of integers".
- Algebraic_integer wikiPageUsesTemplate Template:About.
- Algebraic_integer wikiPageUsesTemplate Template:Algebraic_numbers.
- Algebraic_integer wikiPageUsesTemplate Template:Distinguish.
- Algebraic_integer wikiPageUsesTemplate Template:Math.
- Algebraic_integer wikiPageUsesTemplate Template:Overline.
- Algebraic_integer subject Category:Algebraic_numbers.
- Algebraic_integer subject Category:Integers.
- Algebraic_integer hypernym Number.
- Algebraic_integer type Integer.
- Algebraic_integer type Thing.
- Algebraic_integer comment "In number theory, an algebraic integer is a complex number that is a root of some monic polynomial (a polynomial whose leading coefficient is 1) with coefficients in ℤ (the set of integers). The set of all algebraic integers is closed under addition and multiplication and therefore is a subring of complex numbers denoted by A.".
- Algebraic_integer label "Algebraic integer".
- Algebraic_integer differentFrom Algebraic_element.
- Algebraic_integer differentFrom Algebraic_number.
- Algebraic_integer sameAs Q646245.
- Algebraic_integer sameAs عدد_صحيح_جبري.
- Algebraic_integer sameAs Цэлы_алгебраічны_лік.
- Algebraic_integer sameAs Enter_algebraic.
- Algebraic_integer sameAs Αλγεβρικός_ακέραιος.
- Algebraic_integer sameAs Número_entero_algebraico.
- Algebraic_integer sameAs Algebrallinen_kokonaisluku.
- Algebraic_integer sameAs Entier_algébrique.
- Algebraic_integer sameAs Algebrai_egész_szám.
- Algebraic_integer sameAs Intero_algebrico.
- Algebraic_integer sameAs 代数的整数.
- Algebraic_integer sameAs Бүтін_алгебралық_сан.
- Algebraic_integer sameAs 대수적_정수.
- Algebraic_integer sameAs Алгебралык_бүтүн_сан.
- Algebraic_integer sameAs Algebraïsch_geheel_getal.
- Algebraic_integer sameAs m.0p9j_.
- Algebraic_integer sameAs Целое_алгебраическое_число.
- Algebraic_integer sameAs Ціле_алгебраїчне_число.
- Algebraic_integer sameAs Số_đại_số_nguyên.
- Algebraic_integer sameAs Q646245.
- Algebraic_integer sameAs 代數整數.
- Algebraic_integer wasDerivedFrom Algebraic_integer?oldid=677877219.
- Algebraic_integer isPrimaryTopicOf Algebraic_integer.