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Factorization properties on the composite Hurwitz rings

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강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2024.03|한국수학논문집 (Korean Journal of Mathematics)|제32권 제1호|pp. 97-107

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키워드

Composite Hurwitz ringsunique factorization domainbounded factorization domainfinite factorization domain
주제분류수학

초록

Let $A \subseteq B$ be an extension of integral domains with characteristic zero. Let $H(A,B)$ and $h(A,B)$ be rings of composite Hurwitz series and composite Hurwitz polynomials, respectively. We simply call $H(A,B)$ and $h(A,B)$ composite Hurwitz rings of $A$ and $B$. In this paper, we study when $H(A,B)$ and $h(A,B)$ are unique factorization domains (resp., GCD-domains, finite factorization domains, bounded factorization domains).

Abstract

Let $A \subseteq B$ be an extension of integral domains with characteristic zero. Let $H(A,B)$ and $h(A,B)$ be rings of composite Hurwitz series and composite Hurwitz polynomials, respectively. We simply call $H(A,B)$ and $h(A,B)$ composite Hurwitz rings of $A$ and $B$. In this paper, we study when $H(A,B)$ and $h(A,B)$ are unique factorization domains (resp., GCD-domains, finite factorization domains, bounded factorization domains).

참고문헌 (24)

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관련 논문AI추천

Generalized composite Hurwitz rings as Archimedean domains김동규, 임정욱장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제3호COMPOSITE HURWITZ RINGS AS ARCHIMEDEAN RINGS임정욱영남수학회 · East Asian Mathematical Journal2017 · 제33권 제3호Factorization in the ring $h(\mathbb{Z}, \mathbb{Q})$ of composite Hurwitz polynomials오동렬, 오일목강원경기수학회 · 한국수학논문집2022 · 제30권 제3호Composite Hurwitz Rings Satisfying the Ascending Chain Condition on Principal Ideals오동렬, 임정욱경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제4호Krull dimension of Hurwitz polynomial rings over Pr\"ufer domainsLe Thi Ngoc Giau, Phan Thanh Toan대한수학회 · 대한수학회보2018 · 제55권 제2호Properties of Hurwitz polynomial and Hurwitz series rings김환구, Jesse Elliott대한수학회 · 대한수학회보2018 · 제55권 제3호

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