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- Dedekind_domain abstract "In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily unique up to the order of the factors. There are at least three other characterizations of Dedekind domains that are sometimes taken as the definition: see below.A field is a commutative ring in which there are no nontrivial proper ideals, so that any field is a Dedekind domain, however in a rather vacuous way. Some authors add the requirement that a Dedekind domain not be a field. Many more authors state theorems for Dedekind domains with the implicit proviso that they may require trivial modifications for the case of fields. An immediate consequence of the definition is that every principal ideal domain (PID) is a Dedekind domain. In fact a Dedekind domain is a unique factorization domain (UFD) if and only if it is a PID.".
- Dedekind_domain wikiPageID "145132".
- Dedekind_domain wikiPageLength "22003".
- Dedekind_domain wikiPageOutDegree "73".
- Dedekind_domain wikiPageRevisionID "664905510".
- Dedekind_domain wikiPageWikiLink Abstract_algebra.
- Dedekind_domain wikiPageWikiLink Affine_variety.
- Dedekind_domain wikiPageWikiLink Alan_Baker_(mathematician).
- Dedekind_domain wikiPageWikiLink Algebraic_curve.
- Dedekind_domain wikiPageWikiLink Algebraic_integer.
- Dedekind_domain wikiPageWikiLink Algebraic_integers.
- Dedekind_domain wikiPageWikiLink Algebraic_number.
- Dedekind_domain wikiPageWikiLink Algebraic_number_field.
- Dedekind_domain wikiPageWikiLink Bézout_domain.
- Dedekind_domain wikiPageWikiLink Cambridge_University_Press.
- Dedekind_domain wikiPageWikiLink Carl_Friedrich_Gauss.
- Dedekind_domain wikiPageWikiLink Category:Algebraic_number_theory.
- Dedekind_domain wikiPageWikiLink Category:Commutative_algebra.
- Dedekind_domain wikiPageWikiLink Charles_Leedham-Green.
- Dedekind_domain wikiPageWikiLink Class_number_(number_theory).
- Dedekind_domain wikiPageWikiLink Commutative_ring.
- Dedekind_domain wikiPageWikiLink Coordinate_ring.
- Dedekind_domain wikiPageWikiLink Cyclic_module.
- Dedekind_domain wikiPageWikiLink Diophantine_equation.
- Dedekind_domain wikiPageWikiLink Diophantine_equations.
- Dedekind_domain wikiPageWikiLink Direct_sum_of_modules.
- Dedekind_domain wikiPageWikiLink Discrete_valuation_ring.
- Dedekind_domain wikiPageWikiLink Equivalence_class.
- Dedekind_domain wikiPageWikiLink Ernst_Kummer.
- Dedekind_domain wikiPageWikiLink Ernst_Steinitz.
- Dedekind_domain wikiPageWikiLink Fermats_Last_Theorem.
- Dedekind_domain wikiPageWikiLink Field_(mathematics).
- Dedekind_domain wikiPageWikiLink Field_extension.
- Dedekind_domain wikiPageWikiLink Field_of_fractions.
- Dedekind_domain wikiPageWikiLink Finitely_generated_module.
- Dedekind_domain wikiPageWikiLink Fractional_ideal.
- Dedekind_domain wikiPageWikiLink Gabriel_Lamé.
- Dedekind_domain wikiPageWikiLink Grothendieck_group.
- Dedekind_domain wikiPageWikiLink Harold_Stark.
- Dedekind_domain wikiPageWikiLink Hereditary_ring.
- Dedekind_domain wikiPageWikiLink Ideal_(ring_theory).
- Dedekind_domain wikiPageWikiLink Ideal_class_group.
- Dedekind_domain wikiPageWikiLink Integral_closure.
- Dedekind_domain wikiPageWikiLink Integral_domain.
- Dedekind_domain wikiPageWikiLink Integral_element.
- Dedekind_domain wikiPageWikiLink Integrally_closed_domain.
- Dedekind_domain wikiPageWikiLink Krull_dimension.
- Dedekind_domain wikiPageWikiLink Krull_domain.
- Dedekind_domain wikiPageWikiLink Krull_ring.
- Dedekind_domain wikiPageWikiLink Kurt_Heegner.
- Dedekind_domain wikiPageWikiLink Leonhard_Euler.
- Dedekind_domain wikiPageWikiLink Local_property.
- Dedekind_domain wikiPageWikiLink Local_ring.
- Dedekind_domain wikiPageWikiLink Localization_of_a_ring.
- Dedekind_domain wikiPageWikiLink Maximal_ideal.
- Dedekind_domain wikiPageWikiLink Module_(mathematics).
- Dedekind_domain wikiPageWikiLink Noetherian_domain.
- Dedekind_domain wikiPageWikiLink Noetherian_ring.
- Dedekind_domain wikiPageWikiLink Number_field.
- Dedekind_domain wikiPageWikiLink Oscar_Zariski.
- Dedekind_domain wikiPageWikiLink Pierre_Samuel.
- Dedekind_domain wikiPageWikiLink Pierre_de_Fermat.
- Dedekind_domain wikiPageWikiLink Polynomial.
- Dedekind_domain wikiPageWikiLink Prime_ideal.
- Dedekind_domain wikiPageWikiLink Prime_ideals.
- Dedekind_domain wikiPageWikiLink Principal_ideal_domain.
- Dedekind_domain wikiPageWikiLink Projective_module.
- Dedekind_domain wikiPageWikiLink Proper_ideal.
- Dedekind_domain wikiPageWikiLink Prüfer_domain.
- Dedekind_domain wikiPageWikiLink Quadratic_field.
- Dedekind_domain wikiPageWikiLink Quadratic_form.
- Dedekind_domain wikiPageWikiLink Quadratic_integer.
- Dedekind_domain wikiPageWikiLink Richard_Dedekind.
- Dedekind_domain wikiPageWikiLink Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain.
- Dedekind_domain wikiPageWikiLink Submodule.
- Dedekind_domain wikiPageWikiLink Torsion_(algebra).
- Dedekind_domain wikiPageWikiLink Torsion_submodule.
- Dedekind_domain wikiPageWikiLink Unique_factorization_domain.
- Dedekind_domain wikiPageWikiLinkText "Dedekind domain".
- Dedekind_domain wikiPageWikiLinkText "Dedekind domain#Finitely generated modules over a Dedekind domain".
- Dedekind_domain wikiPageWikiLinkText "uniqueness of prime factorization of the ideals".
- Dedekind_domain hasPhotoCollection Dedekind_domain.
- Dedekind_domain id "p/d030550".
- Dedekind_domain title "Dedekind ring".
- Dedekind_domain wikiPageUsesTemplate Template:Citation.
- Dedekind_domain wikiPageUsesTemplate Template:Cite_book.
- Dedekind_domain wikiPageUsesTemplate Template:Reflist.
- Dedekind_domain wikiPageUsesTemplate Template:Springer.
- Dedekind_domain subject Category:Algebraic_number_theory.
- Dedekind_domain subject Category:Commutative_algebra.
- Dedekind_domain hypernym Domain.
- Dedekind_domain type Protein.
- Dedekind_domain comment "In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily unique up to the order of the factors.".
- Dedekind_domain label "Dedekind domain".
- Dedekind_domain sameAs Dedekindův_obor.
- Dedekind_domain sameAs Dedekindring.
- Dedekind_domain sameAs Dominio_de_Dedekind.
- Dedekind_domain sameAs Anneau_de_Dedekind.
- Dedekind_domain sameAs חוג_דדקינד.
- Dedekind_domain sameAs Dominio_di_Dedekind.