{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-2WIAA2Z8/5a7da453-1b0c-469e-9598-1205e2202fbe/PDF","dcterms:extent":"374 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-2WIAA2Z8/ef728b6f-c461-4244-837b-fb1dece61901/TEXT","dcterms:extent":"27 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-2WIAA2Z8","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":"Pepe, Valentina","dc:format":[{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 515-524"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18962777","URN:URN:NBN:SI:doc-2WIAA2Z8"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"linear sets"},{"@xml:lang":"sl","#text":"linearne množice"},{"@xml:lang":"sl","#text":"polobsegi"},{"@xml:lang":"sl","#text":"razdelitve"},{"@xml:lang":"en","#text":"semifields"},{"@xml:lang":"sl","#text":"simplektična polarnost"},{"@xml:lang":"en","#text":"spreads"},{"@xml:lang":"en","#text":"symplectic polarity"},{"@xml:lang":"en","#text":"Veronese variety"},{"@xml:lang":"sl","#text":"Veronesejeva raznoterost"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Symplectic semifield spreads of PG(5, qsupt), q even|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$q > 2 \\cdot 3^{4t}$? be even. We prove that the only symplectic semifield spread of PG(5, ?$q^t$?), whose associate semifield has center containing ?$\\mathbb{F}_q$?, is the Desarguesian spread. Equivalently, a commutative semifield of order ?$q^{3t}$?, with middle nucleus containing ?$\\mathbb{F}_{q^t}$? and center containing ?$\\mathbb F_q$?, is a field. We do that by proving that the only possible ?$\\mathbb F_q$?-linear set of rank ?$3t$? in PG(5, ?$q^t$?) disjoint from the secant variety of the Veronese surface is a plane of PG(5, ?$q^t$)?"},{"@xml:lang":"sl","#text":"Naj bo ?$q > 2 \\cdot 3^{4t}$? sod. Dokažemo, da je edina simplektična polobsegovna razdelitev projektivnega prostora PG(5, ?$q^t$?), katere pridruženi polobseg ima center, ki vsebuje ?$\\mathbb{F}_q$?, Desarguesova razdelitev. Ekvivalentno, komutativen polobseg reda ?$q^{3t}$? s srednjim nukleusom, ki vsebuje ?$\\mathbb{F}_{q^t}$?, in centrom, ki vsebuje ?$\\mathbb F_q$?, je obseg. To storimo tako, da dokažemo, da je edina možna ?$\\mathbb F_q$?-linearna množica ranga ?$3t$? in PG(5, ?$q^t$?), ki je disjunktna s sekantno raznoterostjo Veronesejeve ploskve, lahko le ravnina v PG(5, ?$q^t$?)"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-2WIAA2Z8","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-2WIAA2Z8"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-2WIAA2Z8/5a7da453-1b0c-469e-9598-1205e2202fbe/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-2WIAA2Z8/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-2WIAA2Z8"}}}}