Factorability in the ring Z[√–5]

Authors

Laura Lynch, Florida Atlantic UniversityFollow

Date of this Version

4-2004

Document Type

Article

Comments

A Thesis presented to the Faculty of The Honors College of Florida Atlantic University In Partial Fulfillment of Requirements for the Degree of Bachelor of Arts in Liberal Arts and Sciences with a Concentration in Mathematics, Under the Supervision of Professor Stephanie Fitchett
Copyright 2004 Laura Lynch

Abstract

The fundamental theorem of arithmetic says that any integer greater than 2 can be written uniquely as a product of primes. For the ring Z[√–5], although unique factorization holds for ideals, unique factorization fails for elements. We investigate both elements and ideals of Z[√–5]. For elements, we examine irreducibility (the analog of primality) in Z[√–5] and look at how often and how badly unique fac- torization fails. For ideals, we examine irreducibility again and a proof for unique factorization.