{"title":"The prime spectrum of an 𝐿-algebra","authors":"Wolfgang Rump, Leandro Vendramin","doi":"10.1090/proc/16802","DOIUrl":null,"url":null,"abstract":"<p>We prove that the lattice of ideals of an arbitrary <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\"application/x-tex\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. the set of prime ideals) of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\"application/x-tex\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-algebras and characterize prime ideals in topological terms.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/proc/16802","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We prove that the lattice of ideals of an arbitrary LL-algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. the set of prime ideals) of LL-algebras and characterize prime ideals in topological terms.
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