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Closure operations on the submonoids of the natural numbers

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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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Title: Closure operations on the submonoids of the natural numbers
Author: Price, Laurie
Advisor(s): Vassilev, Janet
Committee Member(s): Vassilev, Dimiter
Vassilev, Janet
Buium, Alex
Department: University of New Mexico. Dept. of Mathematics and Statistics
Subject(s): Closure operations
Monoids
Natural numbers
Prime operations
Semiprime operations
Submonoids
LC Subject(s): Numbers, Natural.
Closure operators.
Monoids.
Degree Level: Masters
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.
Graduation Date: December 2011
URI: http://hdl.handle.net/1928/17447

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