MATH2017SMITH36813 MATH
Type: Graduate
Author(s):
Jeremy Smith
Mathematics
Advisor(s):
George Gilbert
Mathematics
View PresentationAn algebraic integer is a complex number that is a root of a monic polynomial with integer coefficients. It is well-known that there is not always a single algebraic integer that can generate the ring of algebraic integers contained in a field extension of the rational numbers. The index of an algebraic integer is a natural number that measures how far a ring of integers is from having such a "primitive element." We investigate these indices in cubic fields and determine which natural numbers occur as indices in given families.