On Copure Projective Modules and Copure Projective Dimensions

Fu, Xianhui; Zhu, Hongwei; Ding, Ning

doi:10.1080/00927872.2010.531337

Cited by 15 publications

(17 citation statements)

References 28 publications

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“…(1) ⇒ (2) Let I be a finitely generated ideal of R. Then I is a finitely presented strongly copure flat R-module. By [9,Proposition 3.7], I is strongly copure projective. (5) ⇒ (1) Let E be an injective R-module.…”

Section: Semi-cph Rings and Gorenstein Semihereditary Ringsmentioning

confidence: 99%

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Gorenstein semihereditary rings and Gorenstein Prüfer domains

Xiong¹

2017

International Electronic Journal of Algebra

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Section: Semi-cph Rings and Gorenstein Semihereditary Ringsmentioning

confidence: 99%

“…In [9], Fu et al introduced the concepts of copure projective modules, n-copure projective modules, strongly copure projective modules, and the copure projective dimension. An R-module M is called n-copure…”

Section: Global) Dimension Of Rmentioning

confidence: 99%

Gorenstein semihereditary rings and Gorenstein Prüfer domains

Xiong¹

2017

International Electronic Journal of Algebra

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“…Recall from [7] that a left R-module M is called strongly copure projective if Ext Definition 2.5. ( [6]) Let R be a ring and F a class of R-modules.…”

Section: Preliminariesmentioning

confidence: 99%

“…In [15], Yang described how the homological theory on modules over a Gorenstein ring generalizes to a homological theory on modules over a Ding-Chen ring. Inspired by [7], we will introduce concepts of DP-projective modules, which will be useful to study the Ding projective preenvelope.…”

Section: Introductionmentioning

confidence: 99%

Dp-Projective Modules and Dimensions

Zhao¹

2014

International Electronic Journal of Algebra

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Abstract. In this paper, we introduce the notion of DP-projective modules. It is shown that a left R-module M over a ring R is DP-projective if and only if it is a cokernel of a Ding projective preenvelope f : A → B with B projective. It is also shown that a ring R is semisimple if and only if every module is DP-projective. Moreover, we investigate (global) DP-projective dimensions of modules and rings. It is shown that l.DP -dim(R) = l.DP -ID(R). In addition, other applications of those dimensions defined in this way are presented.Mathematics Subject Classification (2010): 16E10, 16E65, 16Y60

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“…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. …”

mentioning

confidence: 99%