Goldbach's Conjecture in Non-integer Contexts

Goldbach's conjecture, an unproven mathematical claim, states that every even integer greater than 2 can be written as a sum of two prime integers. In this thesis, a more general definition of the conjecture, called the Abstract Goldbach conjecture is proposed, and it is used to extend the study of Goldbach's conjecture outside of the integers proper. The algebra of several non-integer contexts are studied, and Goldbach's conjecture is defined and studied in each of these. In arguing that the conjecture transcends the integers, this work argues that attempts at proving the conjecture should transcend the integers as well.