A classification of graded extensions in a skew Laurent polynomial ring

• Material Type: 記事
• Title: A classification of graded extensions in a skew Laurent polynomial ring
• Author/Editor: Guangming Xie; Hidetoshi Marubayashi
• Author Heading: Guangming Xie; Hidetoshi Marubayashi
• Periodical title: Journal of the Mathematical Society of Japan
• No. or year of volume/issue: 60(2) 2008.4
• Volume: 60
• Issue: 2
• Pages: 423～443
• Publication date of volume/issue (W3CDTF): 2008-04
• ISSN (Periodical Title): 0025-5645
• ISSN-L (Periodical Title): 0025-5645
• Publication (Periodical Title): Tokyo : Mathematical Society of Japan
• Place of Publication (Country Code): JP
• Text Language Code: eng
• Subject Heading: graded extension; total valuation ring; skew Laurent polynomial ring; homogeneous element; division ring
• NDLC: ZM31
• Target Audience: 一般
• Holding library: 国立国会図書館
• Call No.: Z53-A209
• Data Provider (Database): 国立国会図書館 : 国立国会図書館雑誌記事索引; https://ndlsearch.ndl.go.jp
• Bibliographic ID (NDL): 9468081; http://id.ndl.go.jp/bib/9468081
• Bibliographic Record Category (NDL): 632

• Summary, etc.: Let <i>V</i> be a total valuation ring of a division ring <i>K</i> with an automorphism σ and let <i>A</i> = $\oplus$_{i ∈ <b><i>Z</i></b>} <i>A_iXⁱ</i> be a graded extension of <i>V</i> in <i>K</i>[<i>X</i>,<i>X</i>^-1;σ], the skew Laurent polynomial ring. We classify <i>A</i> by distinguishing four different types based on the properties of <i>A</i>₁ and <i>A</i>_-1. A complete description of <i>A_i</i> for all <i>i</i> ∈ <b><i>Z</i></b> is given in the case where <i>A</i>₁ is a finitely generated left <i>O_l</i>(<i>A</i>₁)-ideal.
• DOI: 10.2969/jmsj/06020423
• Access Restrictions: インターネット公開
• Data Provider (Database): 科学技術振興機構 : J-STAGE; http://www.jstage.jst.go.jp

• Summary, etc.: Let <i>V</i> be a total valuation ring of a division ring <i>K</i> with an automorphism σ and let <i>A</i> = $\oplus$_{i ∈ <b><i>Z</i></b>} <i>A_iXⁱ</i> be a graded extension of <i>V</i> in <i>K</i>[<i>X</i>,<i>X</i>^-1;σ], the skew Laurent polynomial ring. We classify <i>A</i> by distinguishing four different types based on the properties of <i>A</i>₁ and <i>A</i>_-1. A complete description of <i>A_i</i> for all <i>i</i> ∈ <b><i>Z</i></b> is given in the case where <i>A</i>₁ is a finitely generated left <i>O_l</i>(<i>A</i>₁)-ideal.
• DOI: 10.2969/jmsj/06020423; https://doi.org/10.2969/jmsj/06020423; 10.2969/jmsj/06141111; https://doi.org/10.2969/jmsj/06141111
• Access Restrictions: インターネット公開
• Related Material (URI): http://id.ndl.go.jp/bib/9468081; https://ndlsearch.ndl.go.jp/books/R000000004-I9468081; http://id.ndl.go.jp/bib/10406348; https://ndlsearch.ndl.go.jp/books/R000000004-I10406348
• References: Valuation Rings in Ore Extensions; https://cir.nii.ac.jp/crid/1360855568883276800; On<i>R</i>-Ideals of a Dubrovin Valuation Ring<i>R</i>; https://cir.nii.ac.jp/crid/1361418520522892288; A classification of prime segments in simple artinian rings; https://cir.nii.ac.jp/crid/1361699993754234368; Extensions of chain rings; https://cir.nii.ac.jp/crid/1361699996421591040; Non-Commutative Valuation Rings and Semi-Hereditary Orders; https://cir.nii.ac.jp/crid/1362262944319566592; Noncommutative Valuation Rings of the Quotient Artinian Ring of a Skew Polynomial Ring; https://cir.nii.ac.jp/crid/1363107369794572928; Gauss extensions and total graded subrings for crossed product algebras; https://cir.nii.ac.jp/crid/1363951794153807104; Non-commutative valuation rings of K(X;σ, δ) over a division ring K; https://cir.nii.ac.jp/crid/1390001205115159936
• Data Provider (Database): 国立情報学研究所 : CiNii Research; https://cir.nii.ac.jp/
• Original Data Provider (Database): Japan Link Center; https://japanlinkcenter.org/top; 雑誌記事索引データベース; https://ndlsearch.ndl.go.jp; Crossref; https://www.crossref.org; CiNii Articles
• Bibliographic ID (NDL): 9468081; http://id.ndl.go.jp/bib/9468081; 10406348; http://id.ndl.go.jp/bib/10406348
• NAID: 10024331698; 10026998641