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Full-Text Articles in Physical Sciences and Mathematics
Multiplicative Sets Of Atoms, Ashley Nicole Rand
Multiplicative Sets Of Atoms, Ashley Nicole Rand
Doctoral Dissertations
It is possible for an element to have both an atom factorization and a factorization that will always contain a reducible element. This leads us to consider the multiplicatively closed set generated by the atoms and units of an integral domain. We start by showing that for a nice subset S of the atoms of R, there exists an integral domain containing R with set of atoms S. A multiplicatively closed set is saturated if the factors of each element in the set are also elements in the set. Considering polynomial and power series subrings, we find necessary and sufficient …
Big Homotopy Theory, Keith Gordon Penrod
Big Homotopy Theory, Keith Gordon Penrod
Doctoral Dissertations
Cannon and Conner developed the theory of "big fundamental groups." This is meant to expand on the notion of fundamental group and is a powerful tool that can be used for distinguishing spaces that are not distinguishable using the fundamental group. Turner proved several classical results, such as covering theory and Seifert-VanKampen for big fundamental groups. The purpose of this paper is to expand on the the theory, to refine the definitions, and to give more examples. Also, in this paper, we define big higher homotopy groups analogous to the way classical higher homotopy groups are defined.