This HTML5 document contains 81 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
yago-reshttp://yago-knowledge.org/resource/
dbohttp://dbpedia.org/ontology/
foafhttp://xmlns.com/foaf/0.1/
n17https://global.dbpedia.org/id/
yagohttp://dbpedia.org/class/yago/
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
freebasehttp://rdf.freebase.com/ns/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
wikipedia-enhttp://en.wikipedia.org/wiki/
dbphttp://dbpedia.org/property/
dbchttp://dbpedia.org/resource/Category:
provhttp://www.w3.org/ns/prov#
xsdhhttp://www.w3.org/2001/XMLSchema#
wikidatahttp://www.wikidata.org/entity/
dbrhttp://dbpedia.org/resource/

Statements

Subject Item
dbr:Partially_ordered_ring
rdf:type
yago:PhysicalEntity100001930 yago:WikicatOrderedAlgebraicStructures yago:Structure104341686 yago:Artifact100021939 yago:YagoGeoEntity yago:Whole100003553 yago:Object100002684 yago:YagoPermanentlyLocatedEntity
rdfs:label
Partially ordered ring
rdfs:comment
In abstract algebra, a partially ordered ring is a ring (A, +, ·), together with a compatible partial order, that is, a partial order on the underlying set A that is compatible with the ring operations in the sense that it satisfies: andfor all . Various extensions of this definition exist that constrain the ring, the partial order, or both. For example, an Archimedean partially ordered ring is a partially ordered ring where 's partially ordered additive group is Archimedean. An l-ring, or lattice-ordered ring, is a partially ordered ring where is additionally a lattice order.
dcterms:subject
dbc:Ordered_algebraic_structures dbc:Ring_theory
dbo:wikiPageID
22211384
dbo:wikiPageRevisionID
1121878632
dbo:wikiPageWikiLink
dbr:Underlying_set dbr:If_and_only_if dbr:Injective dbr:Lattice_order dbr:Total_order dbc:Ordered_algebraic_structures dbr:Image_(mathematics) dbr:Commutative_ring dbr:Archimedean_group dbr:Real_number dbr:Zero_divisor dbr:Topological_space dbr:Garrett_Birkhoff dbr:Partially_ordered_group dbr:Richard_S._Pierce dbr:Real_closed_ring dbr:Trivial_ring dbr:Axiom_of_choice dbr:Direct_product dbr:Hausdorff_space dbr:Category_(mathematics) dbr:IsarMathLib dbr:Maximal_element dbr:Localization_(commutative_algebra) dbr:Function_(mathematics) dbr:Library_(computing) dbr:Continuous_function dbr:Subset dbc:Ring_theory dbr:Ring_(mathematics) dbr:Isabelle_(theorem_prover) dbr:Partial_order dbr:Abstract_algebra dbr:Meyer_Jerison
owl:sameAs
wikidata:Q7140405 freebase:m.05q5t8w yago-res:Partially_ordered_ring n17:4tKg3
dbp:wikiPageUsesTemplate
dbt:SpringerEOM dbt:Short_description dbt:Reflist dbt:Cite_journal dbt:Annotated_link dbt:PlanetMath dbt:Em
dbp:title
Partially Ordered Ring
dbp:urlname
PartiallyOrderedRing
dbo:abstract
In abstract algebra, a partially ordered ring is a ring (A, +, ·), together with a compatible partial order, that is, a partial order on the underlying set A that is compatible with the ring operations in the sense that it satisfies: andfor all . Various extensions of this definition exist that constrain the ring, the partial order, or both. For example, an Archimedean partially ordered ring is a partially ordered ring where 's partially ordered additive group is Archimedean. An ordered ring, also called a totally ordered ring, is a partially ordered ring where is additionally a total order. An l-ring, or lattice-ordered ring, is a partially ordered ring where is additionally a lattice order.
prov:wasDerivedFrom
wikipedia-en:Partially_ordered_ring?oldid=1121878632&ns=0
dbo:wikiPageLength
9450
foaf:isPrimaryTopicOf
wikipedia-en:Partially_ordered_ring
Subject Item
dbr:Real-valued_function
dbo:wikiPageWikiLink
dbr:Partially_ordered_ring
Subject Item
dbr:Totally-ordered_ring
dbo:wikiPageWikiLink
dbr:Partially_ordered_ring
dbo:wikiPageRedirects
dbr:Partially_ordered_ring
Subject Item
dbr:Integer-valued_function
dbo:wikiPageWikiLink
dbr:Partially_ordered_ring
Subject Item
dbr:Garrett_Birkhoff
dbo:wikiPageWikiLink
dbr:Partially_ordered_ring
Subject Item
dbr:Pierce-Birkhoff_ring
dbo:wikiPageWikiLink
dbr:Partially_ordered_ring
dbo:wikiPageRedirects
dbr:Partially_ordered_ring
Subject Item
dbr:Pierce–Birkhoff_ring
dbo:wikiPageWikiLink
dbr:Partially_ordered_ring
dbo:wikiPageRedirects
dbr:Partially_ordered_ring
Subject Item
dbr:Partially-ordered_ring
dbo:wikiPageWikiLink
dbr:Partially_ordered_ring
dbo:wikiPageRedirects
dbr:Partially_ordered_ring
Subject Item
dbr:Lattice-ordered_ring
dbo:wikiPageWikiLink
dbr:Partially_ordered_ring
dbo:wikiPageRedirects
dbr:Partially_ordered_ring
Subject Item
dbr:F-ring
dbo:wikiPageWikiLink
dbr:Partially_ordered_ring
dbo:wikiPageRedirects
dbr:Partially_ordered_ring
Subject Item
wikipedia-en:Partially_ordered_ring
foaf:primaryTopic
dbr:Partially_ordered_ring