{"id":"https://openalex.org/W2496124151","doi":"https://doi.org/10.1007/978-3-8274-2298-9","title":"12 x 12 Schl\u00fcsselkonzepte zur Mathematik","display_name":"12 x 12 Schl\u00fcsselkonzepte zur Mathematik","publication_year":2010,"publication_date":"2010-12-17","ids":{"openalex":"https://openalex.org/W2496124151","doi":"https://doi.org/10.1007/978-3-8274-2298-9","mag":"2496124151"},"language":"de","primary_location":{"id":"doi:10.1007/978-3-8274-2298-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-8274-2298-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306463934","display_name":"Spektrum Akademischer Verlag eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310317836","host_organization_name":"Spektrum Akademischer Verlag","host_organization_lineage":["https://openalex.org/P4310317836"],"host_organization_lineage_names":["Spektrum Akademischer Verlag"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"book"},"type":"book","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086746978","display_name":"Oliver Deiser","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Oliver Deiser","raw_affiliation_strings":["TUM School of Education, Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TUM School of Education, Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084396889","display_name":"Caroline Lasser","orcid":"https://orcid.org/0000-0001-7272-2510"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Caroline Lasser","raw_affiliation_strings":["Zentrum Mathematik - M3 Wissenschaftliches Rechnen, Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zentrum Mathematik - M3 Wissenschaftliches Rechnen, Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012093797","display_name":"Elmar Vogt","orcid":null},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Elmar Vogt","raw_affiliation_strings":["Fachbereich Mathematik und Informatik, Freie Universit\u00e4t Berlin, Berlin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Freie Universit\u00e4t Berlin, Berlin","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109486580","display_name":"Dirk Werner","orcid":null},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dirk Werner","raw_affiliation_strings":["Fachbereich Mathematik und Informatik, Freie Universit\u00e4t Berlin, Berlin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Freie Universit\u00e4t Berlin, Berlin","institution_ids":["https://openalex.org/I75951250"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.30072464,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":94},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.21529999375343323,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.21529999375343323,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6372151374816895},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4602462649345398},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3922508955001831},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2787412405014038}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6372151374816895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4602462649345398},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3922508955001831},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2787412405014038},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-8274-2298-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-8274-2298-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306463934","display_name":"Spektrum Akademischer Verlag eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310317836","host_organization_name":"Spektrum Akademischer Verlag","host_organization_lineage":["https://openalex.org/P4310317836"],"host_organization_lineage_names":["Spektrum Akademischer Verlag"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"book"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-020710310","is_oa":false,"landing_page_url":"http://deposit.dnb.de/cgi-bin/dokserv?id=3477096&prov=M&dok_var=1&dok_ext=htm","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1475110","is_oa":false,"landing_page_url":"https://mediatum.ub.tum.de/1475110","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"book"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2119065487","https://openalex.org/W4234578137"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1979597421","https://openalex.org/W1097487277","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2768610039","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819"],"abstract_inverted_index":{"Wie":[0],"ist":[1],"ein":[2],"Ring":[3],"definiert,":[4],"wann":[5],"kann":[6],"man":[7,17],"Grenzprozesse":[8],"vertauschen,":[9],"was":[10],"sind":[11],"lineare":[12],"Ordnungen":[13],"und":[14],"wozu":[15],"ben\u00f6tigt":[16],"das":[18],"Zornsche":[19],"Lemma":[20],"in":[21],"der":[22],"Linearen":[23],"Algebra?":[24],"Das":[25],"Buch":[26],"will":[27],"seinen":[28],"Lesern":[29],"helfen,":[30],"si":[31]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-27T14:10:00.468798","created_date":"2025-10-10T00:00:00"}