Characteristic modules over a local ring
Let $R$ be a commutative noetherian local ring, and let $M$ be a finitely generated $R$-module. Inspired by works of Vasconcelos and Briggs on characterization of complete intersection local rings through the homological properties of the conormal module, in this paper, we define the characteristic...
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| creator | Gheibi, Mohsen Takahashi, Ryo |
| description | Let $R$ be a commutative noetherian local ring, and let $M$ be a finitely
generated $R$-module. Inspired by works of Vasconcelos and Briggs on
characterization of complete intersection local rings through the homological
properties of the conormal module, in this paper, we define the characteristic
module $\mathrm{T}_M$ and the cocharacteristic module $\mathrm{E}_M$ of $M$,
and investigate their properties. Our main results include characterizations of
Cohen--Macaulay and Gorenstein local rings. |
| doi_str_mv | 10.48550/arxiv.2404.17680 |
| format | Article |
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generated $R$-module. Inspired by works of Vasconcelos and Briggs on
characterization of complete intersection local rings through the homological
properties of the conormal module, in this paper, we define the characteristic
module $\mathrm{T}_M$ and the cocharacteristic module $\mathrm{E}_M$ of $M$,
and investigate their properties. Our main results include characterizations of
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generated $R$-module. Inspired by works of Vasconcelos and Briggs on
characterization of complete intersection local rings through the homological
properties of the conormal module, in this paper, we define the characteristic
module $\mathrm{T}_M$ and the cocharacteristic module $\mathrm{E}_M$ of $M$,
and investigate their properties. Our main results include characterizations of
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generated $R$-module. Inspired by works of Vasconcelos and Briggs on
characterization of complete intersection local rings through the homological
properties of the conormal module, in this paper, we define the characteristic
module $\mathrm{T}_M$ and the cocharacteristic module $\mathrm{E}_M$ of $M$,
and investigate their properties. Our main results include characterizations of
Cohen--Macaulay and Gorenstein local rings.</abstract><doi>10.48550/arxiv.2404.17680</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Commutative Algebra |
| title | Characteristic modules over a local ring |
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