• 제목/요약/키워드: Composite Hurwitz rings

검색결과 4건 처리시간 0.021초

AN ANNIHILATOR CONDITION ON MAXIMAL IDEALS OF COMPOSITE HURWITZ RINGS

  • KIM, DONG KYU;LIM, JUNG WOOK
    • Journal of applied mathematics & informatics
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    • 제38권1_2호
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    • pp.57-64
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    • 2020
  • Let R ⊆ T be an ascending chain of commutative rings with identity and H(R, T) (resp., h(R, T)) the composite Hurwitz series ring (resp., composite Hurwitz polynomial ring). In this article, we give some conditions for the rings H(R, T) and h(R, T) to be PS-rings.

FACTORIZATION PROPERTIES ON THE COMPOSITE HURWITZ RINGS

  • Dong Yeol Oh
    • Korean Journal of Mathematics
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    • 제32권1호
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    • pp.97-107
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    • 2024
  • Let A ⊆ 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).

COMPOSITE HURWITZ RINGS AS ARCHIMEDEAN RINGS

  • Lim, Jung Wook
    • East Asian mathematical journal
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    • 제33권3호
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    • pp.317-322
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    • 2017
  • Let $D{\subseteq}E$ be an extension of integral domains with characteristic zero, I be a nonzero proper ideal of D, and let H(D, E) and H(D, I) (resp., h(D, E) and h(D, I)) be composite Hurwitz series rings (resp., composite Hurwitz polynomial rings). In this article, we show that H(D, E) is an Archimedean ring if and only if h(D, E) is an Archimedean ring, if and only if ${\bigcap}_{n{\geq}1}d^nE=(0)$ for each nonzero nonunit d in D. We also prove that H(D, I) is an Archimedean ring if and only if h(D, I) is an Archimedean ring, if and only if D is an Archimedean ring.

Composite Hurwitz Rings Satisfying the Ascending Chain Condition on Principal Ideals

  • Lim, Jung Wook;Oh, Dong Yeol
    • Kyungpook Mathematical Journal
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    • 제56권4호
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    • pp.1115-1123
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    • 2016
  • Let $D{\subseteq}E$ be an extension of integral domains with characteristic zero, I be a nonzero proper ideal of D and let H(D, E) and H(D, I) (resp., h(D, E) and h(D, I)) be composite Hurwitz series rings (resp., composite Hurwitz polynomial rings). In this paper, we show that H(D, E) satisfies the ascending chain condition on principal ideals if and only if h(D, E) satisfies the ascending chain condition on principal ideals, if and only if ${\bigcap}_{n{\geq}1}a_1{\cdots}a_nE=(0)$ for each infinite sequence $(a_n)_{n{\geq}1}$ consisting of nonzero nonunits of We also prove that H(D, I) satisfies the ascending chain condition on principal ideals if and only if h(D, I) satisfies the ascending chain condition on principal ideals, if and only if D satisfies the ascending chain condition on principal ideals.