Due to the COVID-19 Pandemic, the University has instruction to cancel all in-person events through the Spring semester to adhere to city and state orders limiting public gatherings. Events still running must now take place Online— listed events will include a link in which one may access the Online webspace:

To view Mr. Huth’s defense, enter his Online chatroom via Blackboard Collaborate— it will open at 1:30 pm (30 minutes prior to the event start time) on Tuesday, April 14, 2020.

The Fundamental System of Units for Cubic Number Fields

Mr. Janik Huth
University of Wisconsin-Milwaukee
MS Graduate Student – Teaching Assistant

“Let K be a number field of degree n. An element alpha in K is called integral, if the minimal polynomial of alpha has integer coefficients. The set of all integral elements of K is denoted by O_K . We will prove several properties of this set, e.g. that O_K is a ring and that it has an integral basis. By using a fundamental theorem from algebraic number theory, Dirichlet’s Unit Theorem, we can study the unit group O_K*, defined as the set of all invertible elements of O_K. We will prove Dirichlet’s Unit Theorem and look at unit groups for the special case of cubic number fields of type (1,1). The structure of the unit group allows us to define a fundamental unit for this type of field. We will study the relation between the discriminant of the number field and this fundamental unit.”

Committee Members:
Profs. Allen Bell (Advisor); Jeb Willenbring & Yi Ming Zou

*Click to view the event flyer