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 Committee Member (Chair)
Janet Vassilev
Second Committee Member
Janet Vassilev
Third Committee Member
Alexandru Buium
Language
English
Keywords
Numbers, Natural, Closure operators, Monoids.
Document Type
Thesis
Recommended Citation
Price, Laurie. "Closure operations on the submonoids of the natural numbers." (2012). https://digitalrepository.unm.edu/math_etds/41
