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Almost factoriality
of integral domains and Krull-like domains
Gyu Whan Chang, Hwankoo Kim and Jung Wook Lim |
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Vol. 260 (2012), No. 1, 129–148
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Abstract |
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Let D be an integral domain, D be the integral closure of D, and Γ be a numerical semigroup with Γ ⊊ ℕ0. Let t be the so-called t-operation on D. We will say that D is an AK-domain (resp., AUF-domain) if for each nonzero ideal ({aα}) of D, there exists a positive integer n = n({aα}) such that ({aαn})t is t-invertible (resp., principal). In this paper, we study several properties of AK-domains and AUF-domains. Among other things, we show that if D ⊆ D is a bounded root extension, then D is an AK-domain (resp., AUF-domain) if and only if D is a Krull domain (resp., Krull domain with torsion t-class group) and D is t-linked under D . We also prove that if D is a Krull domain (resp., UFD) with char(D)≠0, then the (numerical) semigroup ring D[Γ] is a nonintegrally closed AK-domain (resp., AUF-domain). |
Keywords
AK-domain, AUF-domain, numerical semigroup, bounded root
extension
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Mathematical Subject Classification 2010
Primary: 13F05
Secondary: 13A15, 13B25, 13G05
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Milestones
Received: 14 January 2012
Revised: 15 March 2012
Accepted: 23 March 2012
Published: 11 October 2012
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Authors |
| Gyu Whan Chang | |
| Department of Mathematics University of Incheon Incheon 406-772 South Korea |
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| Hwankoo Kim | |
| Department of Information
Security Hoseo University Asan 336-795 South Korea |
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| Jung Wook Lim | |
| Department of Mathematics Sogang University Seoul 121-742 South Korea |
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