## Open Access Theses & Dissertations

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.

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#### Provenance

Received from ProQuest

71 pages

application/pdf

Mohamad Moussa

COinS