Multiplicative Sets of Atoms

Author

Ashley Nicole RandFollow

Date of Award

5-2013

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

David F. Anderson

Committee Members

Shashikant Mulay, Luis Finotti, Michael Berry

Abstract

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 conditions for the set generated by the atoms and units to be saturated. We then generalize this to integral domains of the form D+M.

Recommended Citation

Rand, Ashley Nicole, "Multiplicative Sets of Atoms. " PhD diss., University of Tennessee, 2013.
https://trace.tennessee.edu/utk_graddiss/1772