Mathematics Commons^™

Pseudoquotients: Construction, Applications, And Their Fourier Transform, Mehrdad Khosravi

Electronic Theses and Dissertations

A space of pseudoquotients can be described as a space of either single term quotients (the injective case) or the quotient of sequences (the non-injective case) where the parent sets for the numerator and the denominator satisfy particular conditions. The first part of this project is concerned with the minimal of conditions required to have a well-defined set of pseudoquotients. We continue by adding more structure to our sets and discuss the effect on the resultant pseudoquotient. Pseudoquotients can be thought of as extensions of the parent set for the numerator since they include a natural embedding of that set. …