#### Date of Award

2015-01-01

#### Degree Name

Master of Science

#### Department

Mathematical Sciences

#### Advisor(s)

Piotr J. Wojciechowski

#### Abstract

Given a field F and elements \alpha and \beta not in F, then F(\alpha, \beta) is the smallest field containing \alpha,\beta, and F. A simple extension is a field extension which is generated by the adjunction of a single element. The Primitive Element Theorem says that if F is a field of characteristic 0, and \alpha and \beta are algebraic over F, then there is an element \gamma in F(\alpha ,\beta ) such that

F(\alpha ; \beta ) = F(\gamma). When can we say that \gamma=\alpha+\beta? We will introduce some situations where \gamma=\alpha+\beta is true and some when this is not true, where F is the field of rational numbers Q.

#### Language

en

#### Provenance

Received from ProQuest

#### Copyright Date

2015

#### File Size

71 pages

#### File Format

application/pdf

#### Rights Holder

Mohamad Moussa

#### Recommended Citation

Moussa, Mohamad, "When Can The Primitive Element Be Written As A Sum Of Two Algebraic Elements Adjoined To The Field Of The Rational Numbers" (2015). *Open Access Theses & Dissertations*. 1107.

https://scholarworks.utep.edu/open_etd/1107