Hurwitz 다항식 환의 대수적 성질 연구

Abstract

The formal power series rings and polynomial rings have been of interest and have had important applications in many areas including algebra and commutative ring theory. Keigher introduced a variant of the rings of formal power series rings and polynomial rings, and then called them Hurwitz power series rings and Hurwitz polynomial rings, respectively. Since then, many works on the ring of Hurwitz power series and polynomial rings have been done. In this thesis, we introduce a Hurwitz polynomial ring and study its basic algebraic properties. Moreover, we investigate the irreduciblilty of Hurwitz polynomials over the ring of integers and compare those with usual polynomials with integer coefficients.