Statements (52)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Monarch
|
| gptkbp:bfsLayer |
5
|
| gptkbp:bfsParent |
gptkb:Richard_Dedekind
|
| gptkbp:can_be |
a ring where every nonzero proper ideal factors into prime ideals
|
| gptkbp:defines |
a field of fractions
|
| gptkbp:example |
a commutative ring
|
| gptkbp:has_programs |
gptkb:currency
|
| gptkbp:has_property |
every ideal can be factored into prime ideals
|
| https://www.w3.org/2000/01/rdf-schema#label |
Dedekind domain
|
| gptkbp:is_associated_with |
the concept of fractional ideals
|
| gptkbp:is_characterized_by |
every nonzero prime ideal is maximal
the existence of a divisor class group the existence of a unique factorization of ideals the property of being a Dedekind ring. the property of being integrally closed |
| gptkbp:is_connected_to |
localization of rings
|
| gptkbp:is_described_as |
the concept of Dedekind's criterion
|
| gptkbp:is_distinct_from |
of ideals into prime ideals
|
| gptkbp:is_essential_for |
the study of algebraic integers
the development of modern algebra |
| gptkbp:is_involved_in |
a Noetherian domain
|
| gptkbp:is_related_to |
algebraic geometry
the study of Galois theory class groups the concept of ideal class the concept of valuation rings |
| gptkbp:is_represented_in |
a finitely generated module over a Dedekind ring
|
| gptkbp:is_standardized_by |
the ring of integers
|
| gptkbp:is_studied_in |
gptkb:item
|
| gptkbp:is_used_in |
algebraic number theory
the study of algebraic curves the classification of algebraic numbers the proof of unique factorization in number fields |
| gptkbp:key |
number theory
|
| gptkbp:named_after |
gptkb:Richard_Dedekind
|
| gptkbp:related_concept |
abstract algebra
has implications in topology |
| gptkbp:social_structure |
abstract algebra
allows for the study of algebraic integers enables the study of algebraic varieties is foundational in algebraic number theory supports the theory of algebraic integers facilitates the understanding of algebraic extensions |
| gptkbp:type_of |
gptkb:architect
gptkb:Dedekind_ring Noetherian ring local ring commutative Noetherian ring discrete valuation ring integral closure integral domain with certain properties principal ideal domain |