over principal ideal domains, flat modules are exactly torsion-free modules

Full identifier: https://w3id.org/np/RAdMFbkjDyxp6v53Ts4TFNjPj_6kaYiCjQdxcSyijVyp8

 over principal ideal domains, flat modules are exactly torsion-free modules SuperPatternInstance ▼ comment approve/disapprove edit as derived nanopublication create new with same template

this super-pattern instance https://w3id.org/np/RAdMFbkjDy...#spi SPI: links a thing (left) to a class it belongs (right) http://www.w3.org/1999/02/22-rdf-syntax-ns#type This is a a statement that conforms to the super-pattern https://w3id.org/linkflows/superpattern/terms/SuperPatternInstance super-pattern instance .

this super-pattern instance https://w3id.org/np/RAdMFbkjDy...#spi SPI: links a formal identifier (left) to a human-readable name (right) http://www.w3.org/2000/01/rdf-schema#label Informally, it can be shown as (this is a literal) "over principal ideal domains, flat modules are exactly torsion-free modules" .

this super-pattern instance https://w3id.org/np/RAdMFbkjDy...#spi SPI: specifies the context class (right) for the given super-pattern instance (left) https://w3id.org/linkflows/superpattern/terms/hasContextClass In the context of all things of type http://www.wikidata.org/entity/Q1143969 principal ideal domain .

this super-pattern instance https://w3id.org/np/RAdMFbkjDy...#spi SPI: specifies the subject class (right) for the given super-pattern instance (left) https://w3id.org/linkflows/superpattern/terms/hasSubjectClass ... things of type http://www.wikidata.org/entity/Q1426191 flat module .

this super-pattern instance https://w3id.org/np/RAdMFbkjDy...#spi SPI: specifies the qualifier (right) for the given super-pattern statement (left) https://w3id.org/linkflows/superpattern/terms/hasQualifier ... (qualifier) https://w3id.org/linkflows/superpattern/terms/alwaysQualifier always .

this super-pattern instance https://w3id.org/np/RAdMFbkjDy...#spi SPI: specifies the relation type (right) for the given super-pattern statement (left) https://w3id.org/linkflows/superpattern/terms/hasRelation ... have a relation of type https://w3id.org/linkflows/sup...ms/isNecessaryAndSufficientFor is necessary and sufficient for .

this super-pattern instance https://w3id.org/np/RAdMFbkjDy...#spi SPI: specifies the object class (right) for the given super-pattern instance (left) https://w3id.org/linkflows/superpattern/terms/hasObjectClass ... to things of type http://www.wikidata.org/entity/Q7827200 torsion-free module .

This is the identifier for the assertion of this nanopublication. https://w3id.org/np/RAdMFbkjDy...#assertion The assertion above http://www.w3.org/ns/prov#wasAttributedTo is attributed to https://orcid.org/ https://orcid.org/0000-0003-0056-1249 0000-0003-0056-1249 .

This is the identifier for this whole nanopublication. https://w3id.org/np/RAdMFbkjDy... This nanopublication http://purl.org/dc/terms/creator is created by https://orcid.org/0009-0006-3216-8846 me (Uni Marx) .

This is the identifier for this whole nanopublication. https://w3id.org/np/RAdMFbkjDy... This nanopublication http://purl.org/dc/terms/license is published under the license https://creativecommons.org/licenses/by/4.0/ Attribution 4.0 International (CC BY 4.0) .

https://orcid.org/0009-0006-3216-8846 Uni Marx http://xmlns.com/foaf/0.1/name has the name (this is a literal) "Uni Marx" .

This is the identifier for this whole nanopublication. https://w3id.org/np/RAdMFbkjDy... This nanopublication date and time when the nanopublication was created http://purl.org/dc/terms/created was created on (this is a literal) "2024-04-21T18:56:34.886Z" .

This is the identifier for this whole nanopublication. https://w3id.org/np/RAdMFbkjDy... This nanopublication links to the assertion template that was used to create this nanopublication https://w3id.org/np/o/ntemplate/wasCreatedFromTemplate was created from the assertion template http://purl.org/np/RAy3tITXPl... RAy3tITXPl .

This is the identifier for this whole nanopublication. https://w3id.org/np/RAdMFbkjDy... This nanopublication links to the provenance template that was used to create this nanopublication https://w3id.org/np/o/ntemplate/wasCreatedFromProvenanceTemplate was created from the provenance template http://purl.org/np/RAi6zZAwha... RAi6zZAwha .

This is the identifier for this whole nanopublication. https://w3id.org/np/RAdMFbkjDy... This nanopublication links to the publication info template that was used to create this nanopublication https://w3id.org/np/o/ntemplate/wasCreatedFromPubinfoTemplate was created from the publication info template http://purl.org/np/RAA2MfqdBC... RAA2MfqdBC .

This is the identifier for this whole nanopublication. https://w3id.org/np/RAdMFbkjDy... This nanopublication links to the publication info template that was used to create this nanopublication https://w3id.org/np/o/ntemplate/wasCreatedFromPubinfoTemplate was created from the publication info template http://purl.org/np/RAh1gm83Ji... RAh1gm83Ji .

This is the identifier for this whole nanopublication. https://w3id.org/np/RAdMFbkjDy... This nanopublication the nanopublication consists of an introduction of the given resource http://purl.org/nanopub/x/introduces introduces This is a local identifier minted within the nanopublication. https://w3id.org/np/RAdMFbkjDy...#spi spi .

http://www.wikidata.org/entity/Q1143969 principal ideal domain https://w3id.org/np/o/ntemplate/hasLabelFromApi has the label from an API (this is a literal) "principal ideal domain - Algebraic structure" .

http://www.wikidata.org/entity/Q1426191 flat module https://w3id.org/np/o/ntemplate/hasLabelFromApi has the label from an API (this is a literal) "flat module - algebraic structure in ring theory" .

http://www.wikidata.org/entity/Q7827200 torsion-free module https://w3id.org/np/o/ntemplate/hasLabelFromApi has the label from an API (this is a literal) "torsion-free module - module over a ring such that zero is the only element annihilated by a regular element of the ring" .

This is a local identifier minted within the nanopublication. https://w3id.org/np/RAdMFbkjDy...#sig sig http://purl.org/nanopub/x/hasSignatureTarget has as target This is the identifier for this whole nanopublication. https://w3id.org/np/RAdMFbkjDy... this nanopublication .

This is a local identifier minted within the nanopublication. https://w3id.org/np/RAdMFbkjDy...#sig sig http://purl.org/nanopub/x/hasAlgorithm has the algorithm (this is a literal) "RSA" .

This is a local identifier minted within the nanopublication. https://w3id.org/np/RAdMFbkjDy...#sig sig http://purl.org/nanopub/x/hasPublicKey has the public key (this is a literal) "MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCnNLN3ua2JspoEHU8IclouceneexsknOLLz5ONfKbPFteR1TwYn5QQpQgpw/9QBi2xa6EexXYFUJCnol7mEtzmE1+fQO5NKc5MYL/HZxmYlhCCPkuhpe0J9po8C1k8lBOoa0BwoQb1EHlQf4qpaPjgc2jCIXwIkPHiMvLMba/vVQIDAQAB" .

This is a local identifier minted within the nanopublication. https://w3id.org/np/RAdMFbkjDy...#sig sig http://purl.org/nanopub/x/hasSignature has the signature (this is a literal) "lTDlLQzQEeTePcN4KVDSiiuNPrnfFw6UMK85TabmRZKrFKNrgjd8l0h77IrkUuPmdsnXYcZ5y2zT/ejShPHnAGwXf/QOoXK1Qf3D02F15jxPAs72wtc3lr9LVYRugFaASdZF6UPZlR1wWmvPkDcAsNbCmcuBidF4ERpDGRXMhkk=" .

This is a local identifier minted within the nanopublication. https://w3id.org/np/RAdMFbkjDy...#sig sig http://purl.org/nanopub/x/signedBy is signed by https://orcid.org/0009-0006-3216-8846 Uni Marx .

This is the identifier for this whole nanopublication. https://w3id.org/np/RAdMFbkjDy... This nanopublication http://purl.org/nanopub/x/wasCreatedAt was created at https://nanodash.knowledgepixels.com/ nanodash.knowledgepixels.com .

Uni Marx, 21 Apr 2024, 18:56:34 UTC

References