{"?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-NKNNLU12/729d672f-8577-435a-a835-4090eeb5f361/PDF","dcterms:extent":"575 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-NKNNLU12/7068f89e-9609-4e72-b5a1-57315412a9fd/TEXT","dcterms:extent":"106 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-NKNNLU12","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2024","dc:creator":"Vukšić, Lara","dc:format":[{"@xml:lang":"sl","#text":"številka:2, article  p2.04"},{"@xml:lang":"sl","#text":"letnik:24"},{"@xml:lang":"sl","#text":"41 str."}],"dc:identifier":["DOI:10.26493/1855-3974.2968.d23","COBISSID_HOST:169545475","ISSN:1855-3966","URN:URN:NBN:SI:doc-NKNNLU12"],"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":"extensions of orderings"},{"@xml:lang":"en","#text":"extensions of valuations"},{"@xml:lang":"sl","#text":"nekomutativne valuacije"},{"@xml:lang":"sl","#text":"nekomutativni polinomi"},{"@xml:lang":"en","#text":"noncommutative valuations"},{"@xml:lang":"en","#text":"orderings"},{"@xml:lang":"sl","#text":"razširitve urejenosti"},{"@xml:lang":"sl","#text":"razširitve valuacij"},{"@xml:lang":"en","#text":"skew polynomial rings"},{"@xml:lang":"sl","#text":"urejenost"},{"@xml:lang":"en","#text":"Weyl algebra"},{"@xml:lang":"sl","#text":"Weylova algebra"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Valuations and orderings on the real Weyl algebra|"},"dc:description":{"@xml:lang":"sl","#text":"The first Weyl algebra ?${\\cal A}_1(k)$? over a field ?$k$? is the ?$k$?-algebra with two generators ?$x, y$? subject to ?$y, x = 1$? and was first introduced during the development of quantum mechanics. In this article, we classify all valuations on the real Weyl algebra ?${\\cal A}_1({\\mathbb R})$? whose residue field is ?${\\mathbb R}$?. We then use a noncommutative version of the Baer-Krull theorem to classify all orderings on ?${\\cal A}_1({\\mathbb R})$?. As a byproduct of our studies, we settle two open problems in real algebraic geometry. First, we show that not all orderings on ?${\\cal A}_1({\\mathbb R})$? extend to an ordering on a larger ring ?$Ry; \\delta$?, where ?$R$? is the ring of Puiseux series, introduced by Marshall and Zhang in 2000, and characterize the orderings that do have such an extension. Second, we show that for valuations on noncommutative division rings, Kaplansky’s theorem that extensions by limits of pseudo-Cauchy sequences are immediate fails in general"},"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-NKNNLU12","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-NKNNLU12"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-NKNNLU12/729d672f-8577-435a-a835-4090eeb5f361/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-NKNNLU12/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-NKNNLU12"}}}}