Show simple item record

dc.contributor.authorPrice, Laurie
dc.date.accessioned2012-02-01T17:29:31Z
dc.date.available2012-02-01T17:29:31Z
dc.date.issued2012-02-01
dc.date.submittedDecember 2011
dc.identifier.urihttp://hdl.handle.net/1928/17447
dc.description.abstractWe examine the algebraic structure of closure, semiprime and prime operations on submonoids of natural numbers. We find that the closure operations under composition do not form a submonoid under composition. We also describe all the semiprime operations on natural numbers and show that they are a submonoid. We investigate the relations among the semiprime operations on ideals of the sub- semi-group (2, 3) and define which of these operations may form a monoid or a left act under composition. We also consider the algebraic structure of monoids with multiple maximal ideals and generalize these results to higher dimensions.en_US
dc.language.isoen_USen_US
dc.subjectClosure operationsen_US
dc.subjectMonoidsen_US
dc.subjectNatural numbersen_US
dc.subjectPrime operationsen_US
dc.subjectSemiprime operationsen_US
dc.subjectSubmonoidsen_US
dc.subject.lcshNumbers, Natural.
dc.subject.lcshClosure operators.
dc.subject.lcshMonoids.
dc.titleClosure operations on the submonoids of the natural numbersen_US
dc.typeThesisen_US
dc.description.degreeMathematicsen_US
dc.description.levelMastersen_US
dc.description.departmentUniversity of New Mexico. Dept. of Mathematics and Statisticsen_US
dc.description.advisorVassilev, Janet
dc.description.committee-memberVassilev, Dimiter
dc.description.committee-memberVassilev, Janet
dc.description.committee-memberBuium, Alex
dc.data.json{ "@context": { "rdf": "http://www.w3.org/1999/02/22-rdf-syntax-ns#", "rdfs": "http://www.w3.org/2000/01/rdf-schema#", "xsd": "http://www.w3.org/2001/XMLSchema#" }, "@graph": [ { "@id": "http://54.191.234.158/entities/resource/Price_Laurie", "@type": "http://schema.org/Person" }, { "@id": "http://54.191.234.158/entities/resource/Natural_numbers", "@type": "http://schema.org/Intangible" }, { "@id": "http://54.191.234.158/entities/resource/Monoids", "@type": "http://schema.org/Intangible" }, { "@id": "http://54.191.234.158/entities/resource/Submonoids", "@type": "http://schema.org/Intangible" }, { "@id": "http://54.191.234.158/entities/resource/Closure_operations", "@type": "http://schema.org/Intangible" }, { "@id": "http://hdl.handle.net/1928/6670", "@type": "http://schema.org/WebSite" }, { "@id": "http://54.191.234.158/entities/resource/Semiprime_operations", "@type": "http://schema.org/Intangible" }, { "@id": "http://hdl.handle.net/1928/17447", "@type": "http://schema.org/CreativeWork", "http://purl.org/montana-state/library/associatedDepartment": { "@id": "http://54.191.234.158/entities/resource/University_of_New_Mexico.__Dept._of_Mathematics_and_Statistics" }, "http://purl.org/montana-state/library/degreeGrantedForCompletion": "Mathematics", "http://purl.org/montana-state/library/hasEtdCommitee": { "@id": "http://54.191.234.158/entities/resource/1928/17447" }, "http://schema.org/about": [ { "@id": "http://54.191.234.158/entities/resource/Numbers_Natural." }, { "@id": "http://54.191.234.158/entities/resource/Prime_operations" }, { "@id": "http://54.191.234.158/entities/resource/Closure_operations" }, { "@id": "http://54.191.234.158/entities/resource/Closure_operators" }, { "@id": "http://54.191.234.158/entities/resource/Monoids." }, { "@id": "http://54.191.234.158/entities/resource/Monoids" }, { "@id": "http://54.191.234.158/entities/resource/Semiprime_operations" }, { "@id": "http://54.191.234.158/entities/resource/Natural_numbers" }, { "@id": "http://54.191.234.158/entities/resource/Submonoids" } ], "http://schema.org/author": { "@id": "http://54.191.234.158/entities/resource/Price_Laurie" }, "http://schema.org/dateCreated": "December 2011", "http://schema.org/datePublished": "2012-02-01", "http://schema.org/description": "We examine the algebraic structure of closure, semiprime and prime operations on submonoids of natural numbers. We find that the closure operations under composition do not form a submonoid under composition. We also describe all the semiprime operations on natural numbers and show that they are a submonoid.\nWe investigate the relations among the semiprime operations on ideals of the sub- semi-group (2, 3) and define which of these operations may form a monoid or a left act under composition.\nWe also consider the algebraic structure of monoids with multiple maximal ideals and generalize these results to higher dimensions.", "http://schema.org/inLanguage": "en_US", "http://schema.org/isPartOf": { "@id": "http://hdl.handle.net/1928/6670" }, "http://schema.org/name": "Closure operations on the submonoids of the natural numbers" }, { "@id": "http://54.191.234.158/entities/resource/Closure_operators", "@type": "http://schema.org/Intangible" }, { "@id": "http://54.191.234.158/entities/resource/Numbers_Natural.", "@type": "http://schema.org/Intangible" }, { "@id": "http://54.191.234.158/entities/resource/Prime_operations", "@type": "http://schema.org/Intangible" }, { "@id": "http://54.191.234.158/entities/resource/Monoids.", "@type": "http://schema.org/Intangible" } ]}


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record