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Closure operations on the submonoids of the natural numbers


Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/17447

Closure operations on the submonoids of the natural numbers

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dc.contributor.author Price, Laurie
dc.date.accessioned 2012-02-01T17:29:31Z
dc.date.available 2012-02-01T17:29:31Z
dc.date.issued 2012-02-01
dc.date.submitted December 2011
dc.identifier.uri http://hdl.handle.net/1928/17447
dc.description.abstract 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. 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.iso en_US en_US
dc.subject Closure operations en_US
dc.subject Monoids en_US
dc.subject Natural numbers en_US
dc.subject Prime operations en_US
dc.subject Semiprime operations en_US
dc.subject Submonoids en_US
dc.subject.lcsh Numbers, Natural.
dc.subject.lcsh Closure operators.
dc.subject.lcsh Monoids.
dc.title Closure operations on the submonoids of the natural numbers en_US
dc.type Thesis en_US
dc.description.degree Mathematics en_US
dc.description.level Masters en_US
dc.description.department University of New Mexico. Dept. of Mathematics and Statistics en_US
dc.description.advisor Vassilev, Janet
dc.description.committee-member Vassilev, Dimiter
dc.description.committee-member Vassilev, Janet
dc.description.committee-member Buium, Alex

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