The construction D + XDS  [X] and G-Prüfer domains

Kui Hu; Jung Wook Lim; De Chuan Zhou

doi:10.1080/00927872.2023.2200837

The construction D + XD_S [X] and G-Prüfer domains

Kui Hu
, Jung Wook Lim
, De Chuan Zhou

Southwest University of Science and Technology

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

Abstract

Let D be an integral domain with quotient field K, S a (not necessarily saturated) multiplicative subset of D and (Formula presented.). In this paper, we show that (Formula presented.) is a G-Prüfer domain if and only if D is a G-Prüfer domain and D_S = K. We also prove that if D is a Bass domain (or a local NWF domain), then every finitely generated torsion-free module over (Formula presented.) is isomorphic to a direct sum of some ideals.

Original language	English
Pages (from-to)	4195-4203
Number of pages	9
Journal	Communications in Algebra
Volume	51
Issue number	10
DOIs	https://doi.org/10.1080/00927872.2023.2200837
State	Published - 2023

Keywords

Bass domains
G-Prüfer domain
SG-projective modules
weakly SG-hereditary domains

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10.1080/00927872.2023.2200837

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title = "The construction D + XDS [X] and G-Pr{\"u}fer domains",

abstract = "Let D be an integral domain with quotient field K, S a (not necessarily saturated) multiplicative subset of D and (Formula presented.). In this paper, we show that (Formula presented.) is a G-Pr{\"u}fer domain if and only if D is a G-Pr{\"u}fer domain and DS = K. We also prove that if D is a Bass domain (or a local NWF domain), then every finitely generated torsion-free module over (Formula presented.) is isomorphic to a direct sum of some ideals.",

keywords = "Bass domains, G-Pr{\"u}fer domain, SG-projective modules, weakly SG-hereditary domains",

author = "Kui Hu and Lim, \{Jung Wook\} and Zhou, \{De Chuan\}",

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T1 - The construction D + XDS [X] and G-Prüfer domains

AU - Hu, Kui

AU - Lim, Jung Wook

AU - Zhou, De Chuan

PY - 2023

Y1 - 2023

N2 - Let D be an integral domain with quotient field K, S a (not necessarily saturated) multiplicative subset of D and (Formula presented.). In this paper, we show that (Formula presented.) is a G-Prüfer domain if and only if D is a G-Prüfer domain and DS = K. We also prove that if D is a Bass domain (or a local NWF domain), then every finitely generated torsion-free module over (Formula presented.) is isomorphic to a direct sum of some ideals.

AB - Let D be an integral domain with quotient field K, S a (not necessarily saturated) multiplicative subset of D and (Formula presented.). In this paper, we show that (Formula presented.) is a G-Prüfer domain if and only if D is a G-Prüfer domain and DS = K. We also prove that if D is a Bass domain (or a local NWF domain), then every finitely generated torsion-free module over (Formula presented.) is isomorphic to a direct sum of some ideals.

KW - Bass domains

KW - G-Prüfer domain

KW - SG-projective modules

KW - weakly SG-hereditary domains

UR - https://www.scopus.com/pages/publications/85153495861

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DO - 10.1080/00927872.2023.2200837

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SP - 4195

EP - 4203

JO - Communications in Algebra

JF - Communications in Algebra

IS - 10

ER -

The construction D + XD_S [X] and G-Prüfer domains

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Keywords

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