Rings whose ideals are isomorphic to trace ideals
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- Toshinori Kobayashi
- Graduate School of Mathematics Nagoya University Furocho, Chikusaku Nagoya Aichi 464‐8602 Japan
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- Ryo Takahashi
- Graduate School of Mathematics Nagoya University Furocho, Chikusaku Nagoya Aichi 464‐8602 Japan
Abstract
<jats:title>Abstract</jats:title><jats:p>Let <jats:italic>R</jats:italic> be a commutative noetherian ring. Lindo and Pande have recently posed the question asking when every ideal of <jats:italic>R</jats:italic> is isomorphic to some trace ideal of <jats:italic>R</jats:italic>. This paper studies this question and gives several answers. In particular, a complete answer is given in the case where <jats:italic>R</jats:italic> is local: it is proved in this paper that every ideal of <jats:italic>R</jats:italic> is isomorphic to a trace ideal if and only if <jats:italic>R</jats:italic> is an artinian Gorenstein ring, or a 1‐dimensional hypersurface with multiplicity at most 2, or a unique factorization domain.</jats:p>
Journal
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- Mathematische Nachrichten
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Mathematische Nachrichten 292 (10), 2252-2261, 2019-07-15
Wiley
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Details 詳細情報について
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- CRID
- 1361131414697601280
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- ISSN
- 15222616
- 0025584X
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- Data Source
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- Crossref
- KAKEN