정수환 Z상의 Hurwitz 다항식의 기약성 연구

Abstract

The formal power series rings and polynomial rings have been of interest and have had important applications in commutative ring theory. As generalizations of formal power series and polynomial rings, semigroup rings and graded rings are investigated. As another point of view of generalization of formal power series and polynomial rings, Keigher introduced Hurwitz power series rings and Hurwitz polynomial rings, respectively. Affer keigher many researches on the ring of Hurwitz power series and polynomial rings have been done. In this thesis, we introduce a Hurwitz polynomial ring and study the irreduciblity of Hurwitz polynomials over We also investigate the irreduciblilty of Hurwitz polynomials of higher degree greater than equal to 3 over the ring of integers. More precisely, by using a relation between Hurwitz polynomial over the ring of integers and usual polynomials over the ring of integers, we give a necessary and sufficient condition for Hurwitz polynomials of higher degree greater than equal to 3 over the ring of integers to be irreducible.