A note on two-generated ideals over domains

Kui Hu; Jung Wook Lim; De Chuan Zhou

doi:10.1142/S0219498822502462

A note on two-generated ideals over domains

Kui Hu, Jung Wook Lim, De Chuan Zhou

Research output: Contribution to journal › Article › peer-review

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Abstract

Let R be a one-dimensional Noetherian domain and I be a two-generated fractional ideal of R. In this paper, we prove that I is SG-projective if and only if I and I-1 are equivalent, i.e.There exists a projective fractional ideal P of R such that I = I-1P. We also give an example to show that I being SG-projective does not necessarily imply that I and I-1 are isomorphic.

Original language	English
Article number	2250246
Journal	Journal of Algebra and its Applications
Volume	21
Issue number	10
DOIs	https://doi.org/10.1142/S0219498822502462
State	Published - 1 Oct 2022

Keywords

equivalent relation âon fractional ideals
S G-projective
two-generated ideals

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10.1142/S0219498822502462

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abstract = "Let R be a one-dimensional Noetherian domain and I be a two-generated fractional ideal of R. In this paper, we prove that I is SG-projective if and only if I and I-1 are equivalent, i.e.There exists a projective fractional ideal P of R such that I = I-1P. We also give an example to show that I being SG-projective does not necessarily imply that I and I-1 are isomorphic.",

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AU - Zhou, De Chuan

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N2 - Let R be a one-dimensional Noetherian domain and I be a two-generated fractional ideal of R. In this paper, we prove that I is SG-projective if and only if I and I-1 are equivalent, i.e.There exists a projective fractional ideal P of R such that I = I-1P. We also give an example to show that I being SG-projective does not necessarily imply that I and I-1 are isomorphic.

AB - Let R be a one-dimensional Noetherian domain and I be a two-generated fractional ideal of R. In this paper, we prove that I is SG-projective if and only if I and I-1 are equivalent, i.e.There exists a projective fractional ideal P of R such that I = I-1P. We also give an example to show that I being SG-projective does not necessarily imply that I and I-1 are isomorphic.

KW - equivalent relation âon fractional ideals

KW - S G-projective

KW - two-generated ideals

UR - https://www.scopus.com/pages/publications/85129047248

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DO - 10.1142/S0219498822502462

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VL - 21

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

IS - 10

M1 - 2250246

ER -

A note on two-generated ideals over domains

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Keywords

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