NON-COMMUTATIVE KRULL MONOIDS :  A DIVISOR THEORETIC APPROACH AND THEIR ARITHMETIC

Geroldinger, Alfred

doi:https://doi.org/10.18910/25092

NON-COMMUTATIVE KRULL MONOIDS : A DIVISOR THEORETIC APPROACH AND THEIR ARITHMETIC

Geroldinger, Alfred

Osaka Journal of Mathematics, 2013, 50(2), 503-539

アクセス数:164件（2025-04-29 15:39 集計）

固定URL: https://doi.org/10.18910/25092

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タイトル	NON-COMMUTATIVE KRULL MONOIDS : A DIVISOR THEORETIC APPROACH AND THEIR ARITHMETIC
著者	著者名 Geroldinger, Alfred
抄録	A (not necessarily commutative) Krull monoid─as introduced by Wauters─is defined as a completely integrally closed monoid satisfying the ascending chain condition on divisorial two-sided ideals. We study the structure of these Krull monoids, both with ideal theoretic and with divisor theoretic methods. Among others we characterize normalizing Krull monoids by divisor theories. Based on these results we give a criterion for a Krull monoid to be a bounded factorization monoid, and we provide arithmetical finiteness results in case of normalizing Krull monoids with finite Davenport constant.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	50(2)
ページ	503-539
刊行年月	2013-06
言語	英語
ハンドルURL	https://hdl.handle.net/11094/25092
DOI	https://doi.org/10.18910/25092
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 50, Number 2　(2013-6）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2013, 50(2), p. 503-539
DC.title	NON-COMMUTATIVE KRULL MONOIDS : A DIVISOR THEORETIC APPROACH AND THEIR ARITHMETIC
DC.creator	Geroldinger, Alfred
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2013-06
DCTERMS.abstract	A (not necessarily commutative) Krull monoid─as introduced by Wauters─is defined as a completely integrally closed monoid satisfying the ascending chain condition on divisorial two-sided ideals. We study the structure of these Krull monoids, both with ideal theoretic and with divisor theoretic methods. Among others we characterize normalizing Krull monoids by divisor theories. Based on these results we give a criterion for a Krull monoid to be a bounded factorization monoid, and we provide arithmetical finiteness results in case of normalizing Krull monoids with finite Davenport constant.
DC.identifier	10.18910/25092
DC.format	25092
citation_title	NON-COMMUTATIVE KRULL MONOIDS : A DIVISOR THEORETIC APPROACH AND THEIR ARITHMETIC
citation_author	Geroldinger, Alfred
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2013-06
citation_journal_title	Osaka Journal of Mathematics
citation_volume	50
citation_issue	2
citation_firstpage	503
citation_lastpage	539
citation_public_url	https://hdl.handle.net/11094/25092
citation_doi_detail	10.18910/25092
citation_doi	https://doi.org/10.18910/25092

NON-COMMUTATIVE KRULL MONOIDS : A DIVISOR THEORETIC APPROACH AND THEIR ARITHMETIC

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