Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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FACTORIZATION IN THE RING h(ℤ, ℚ) OF COMPOSITE HURWITZ POLYNOMIALS

  • Oh, Dong Yeol (Department of Mathematics Education, Chosun University) ;
  • Oh, Ill Mok (Department of Mathematics Education, Chosun University)
  • Received : 2022.03.31
  • Accepted : 2022.07.29
  • Published : 2022.09.30
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Abstract

Let ℤ and ℚ be the ring of integers and the field of rational numbers, respectively. Let h(ℤ, ℚ) be the ring of composite Hurwitz polynomials. In this paper, we study the factorization of composite Hurwitz polynomials in h(ℤ, ℚ). We show that every nonzero nonunit element of h(ℤ, ℚ) is a finite *-product of quasi-primary elements and irreducible elements of h(ℤ, ℚ). By using a relation between usual polynomials in ℚ[x] and composite Hurwitz polynomials in h(ℤ, ℚ), we also give a necessary and sufficient condition for composite Hurwitz polynomials of degree ≤ 3 in h(ℤ, ℚ) to be irreducible.

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Acknowledgement

We would like to thank the referees for several valuable suggestions. This paper (Section 3) contains part of a master's thesis of I.M.Oh done at Chosun University.

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