The construction of all the star operations and all the semistar operations on 1-dimensional Prüfer domains
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- Matsuda Ryûki
- Ibaraki University
抄録
Let Σ(D) (resp., Σ ′ (D)) be the set of star (resp., semistar) operations on a domain D. E. Houston gave necessary and sufficient conditions for an integrally closed domain D to have |Σ(D)| < ∞. Moreover, under those conditions, he gave the cardinality |Σ(<i>D</i>)| (Booklet of Abstracts of Conference: Commutative Rings and their Modules, 2012, Bressanone, Italy). We proved that an integrally closed domain D has <i>|Σ ' </i>(<i>D</i>)<i>| </i>< ∞ if and only if it is a finite dimensional Prüfer domain with finitely many maximal ideals. Also we gave conditions for a pseudo-valuation domain (resp., an almost pseudo-valuation domain) D to have <i><i>|Σ ' </i></i>(<i><i>D</i></i>)<i><i>| </i>< ∞</i>. In this paper, we study star and semistar operations on a 1-dimensional Prüfer domain D. We aim to construct all the star and semistar operations on D. We introduce a sigma operation on D, and show that every semistar operation on D is expressed as a unique product of a star operation and a sigma operation.
収録刊行物
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- Mathematical journal of Ibaraki University
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Mathematical journal of Ibaraki University 47 (0), 19-37, 2015
茨城大学 理学部 数学教室
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詳細情報 詳細情報について
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- CRID
- 1390001205274950912
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- NII論文ID
- 130005100040
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- ISSN
- 18834353
- 13433636
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- Crossref
- CiNii Articles
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- 抄録ライセンスフラグ
- 使用不可