Sets of Lengths Over Residue Class Rings of the Integers

Author

Daniel B. Kline

Date of Graduation

Spring 2011

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Mark Rogers

Abstract

Factorization in Z_p^n[x] is patently non-unique. In this paper we examine properties of what we call generalized Eisenstein polynomials in Z_p^2[x]. We prove an irreducibility result and compute the set of lengths of every generalized Eisenstein polynomial in Z_p^2[x].

Keywords

sets of lengths, non-unique factorization, irreducible, Eisenstein polynomials, powers of x

Subject Categories

Mathematics

Copyright

© Daniel B. Kline

Recommended Citation

Kline, Daniel B., "Sets of Lengths Over Residue Class Rings of the Integers" (2011). MSU Graduate Theses/Dissertations. 1638.
https://bearworks.missouristate.edu/theses/1638