Author

Laurie Price

Publication Date

2-1-2012

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.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Advisor

Vassilev, Janet

First Committee Member (Chair)

Vassilev, Dimiter

Second Committee Member

Vassilev, Janet

Third Committee Member

Buium, Alex

Language

English

Keywords

Numbers, Natural, Closure operators, Monoids.

Document Type

Thesis

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