A Note on Local Weakly SG-Hereditary Domains

Kui Hu; Jung Wook Lim; De Chuan Zhou

doi:10.1007/s41980-019-00311-6

A Note on Local Weakly SG-Hereditary Domains

Kui Hu
, Jung Wook Lim
, De Chuan Zhou

Southwest University of Science and Technology
Kyungpook National University

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

3 Scopus citations

Abstract

A ring R is called weakly SG-hereditary if every ideal of R is SG-projective. In this note, we prove that a local domain R is a Noetherian Warfield domain if and only if it is weakly SG-hereditary. Furthermore, we prove that any countably generated submodule of any free module over a Noetherian local Warfield domain is SG-projective.

Original language	English
Pages (from-to)	1045-1054
Number of pages	10
Journal	Bulletin of the Iranian Mathematical Society
Volume	46
Issue number	4
DOIs	https://doi.org/10.1007/s41980-019-00311-6
State	Published - 1 Aug 2020

Keywords

Noetherian local Warfield domains
SG-Dedekind domains
Weakly SG-hereditary rings

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10.1007/s41980-019-00311-6

Cite this

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title = "A Note on Local Weakly SG-Hereditary Domains",

abstract = "A ring R is called weakly SG-hereditary if every ideal of R is SG-projective. In this note, we prove that a local domain R is a Noetherian Warfield domain if and only if it is weakly SG-hereditary. Furthermore, we prove that any countably generated submodule of any free module over a Noetherian local Warfield domain is SG-projective.",

keywords = "Noetherian local Warfield domains, SG-Dedekind domains, Weakly SG-hereditary rings",

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AU - Lim, Jung Wook

AU - Zhou, De Chuan

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N2 - A ring R is called weakly SG-hereditary if every ideal of R is SG-projective. In this note, we prove that a local domain R is a Noetherian Warfield domain if and only if it is weakly SG-hereditary. Furthermore, we prove that any countably generated submodule of any free module over a Noetherian local Warfield domain is SG-projective.

AB - A ring R is called weakly SG-hereditary if every ideal of R is SG-projective. In this note, we prove that a local domain R is a Noetherian Warfield domain if and only if it is weakly SG-hereditary. Furthermore, we prove that any countably generated submodule of any free module over a Noetherian local Warfield domain is SG-projective.

KW - Noetherian local Warfield domains

KW - SG-Dedekind domains

KW - Weakly SG-hereditary rings

UR - https://www.scopus.com/pages/publications/85074269738

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JF - Bulletin of the Iranian Mathematical Society

IS - 4

ER -

A Note on Local Weakly SG-Hereditary Domains

Abstract

Keywords

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