Non-commutative valuation rings of K (X ; σ, δ) over a division ring K

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Let K be a division ring with a σ-derivation δ, where σ is an endomor-phism of K and K(X;σ, δ) be the quotient division ring of the Ore extension K[X;σ, δ] over K in an indeterminate X. First, we describe non-commutative valuation rings of K(X;σ, δ) which contain K[X;σ, δ]. Suppose that (σ, δ) is compatible with V, where V is a total valuation ring of K, then R<SUP>(1)</SUP>=V[X;σ, δ]_{J(V)[X;σ, δ]}, the localization of V[X;σ, δ] at J(V)[X;σ, δ], is a total valuation ring of K(X;σ, δ). Applying the description above, then, second, we describe non-commutative valuation rings B of K(X;σ, δ) such that B∩ K=V, X∈ B and B⊂eq R<SUP>(1)</SUP>, which is the aim of this paper. In the end of each section we give several examples to display some of the various phenomena.

収録刊行物

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 56(3), 737-752, 2004-07-01

    一般社団法人 日本数学会

参考文献:  18件中 1-18件 を表示

被引用文献:  2件中 1-2件 を表示

各種コード

  • NII論文ID(NAID)
    10013358908
  • NII書誌ID(NCID)
    AA0070177X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    00255645
  • NDL 記事登録ID
    7015141
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z53-A209
  • データ提供元
    CJP書誌  CJP引用  NDL  J-STAGE 
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