Rings of Copure Projective Dimension One

Xiong, Tao

doi:10.4134/jkms.j160014

Journal of the Korean Mathematical Society

2017

DOI: 10.4134/jkms.j160014

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Rings of Copure Projective Dimension One

Tao Xiong¹

Abstract: Abstract. In this paper, in terms of the notions of strongly copure projective modules and the copure projective dimension cpD(R) of a ring R were defined in [12], we show that a domain R has cpD(R) ≤ 1 if and only if R is a Gorenstein Dedekind domain.

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“…In [33,35], Xiong et al proved that a ring R has cpD(R) ≤ 1 if and only if every submodule of a projective R-module is copure projective. In this case, R is said to be a CPH (Copure-Projective-Hereditary) ring provisionally.…”

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confidence: 99%

Gorenstein semihereditary rings and Gorenstein Prüfer domains

Xiong¹

2017

International Electronic Journal of Algebra

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mentioning

confidence: 99%

Gorenstein semihereditary rings and Gorenstein Prüfer domains

Xiong¹

2017

International Electronic Journal of Algebra

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On w -copure projective modules

Assaad,

Tamekkante,

Mao

2023

Communications in Algebra

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Almost Gorenstein Dedekind domains

Xing

Kim

et al. 2023

J. Algebra Appl.

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An integral domain [Formula: see text] is said to be locally G-Dedekind if the Gorenstein global dimension of [Formula: see text] is at most one for each maximal ideal [Formula: see text]. In this paper, we show that an integral domain [Formula: see text] is not necessarily a G-Prüfer even if [Formula: see text] is a locally G-Dedekind domain, which gives a negative answer to the question raised by the first author. It follows that the localization of the G-Prüfer domain differs from the classical case of the Prüfer domain. We also study coherent locally G-Dedekind domains, called almost G-Dedekind domains. The almost G-Dedekind domains need not be integrally closed and fill the gap between the G-Dedekind domains and the G-Prüfer domains. Various examples are provided to illustrate the new concept.

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Rings of Copure Projective Dimension One

Abstract: Abstract. In this paper, in terms of the notions of strongly copure projective modules and the copure projective dimension cpD(R) of a ring R were defined in [12], we show that a domain R has cpD(R) ≤ 1 if and only if R is a Gorenstein Dedekind domain.

Cited by 3 publications

References 3 publications

Gorenstein semihereditary rings and Gorenstein Prüfer domains

Gorenstein semihereditary rings and Gorenstein Prüfer domains

On w -copure projective modules

Almost Gorenstein Dedekind domains

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