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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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.",

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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.

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KW - G-Prüfer domain

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

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Keywords

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