Finitely generated G-projective modules over PVMDS

Kui Hu; Jung Wook Lim; Shiqi Xing

doi:10.4134/BKMS.b190531

Finitely generated G-projective modules over PVMDS

Kui Hu
, Jung Wook Lim
, Shiqi Xing

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

Abstract

Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ: M⊗_RM^* → Hom_R(Hom_R(M,M),R) is a surjective homomorphism. Particularly, if G-gldim(R) ≤ ∞ and Extⁱ _R(M,M) = 0 (i ≥ 1), then M is projective.

Original language	English
Pages (from-to)	803-813
Number of pages	11
Journal	Bulletin of the Korean Mathematical Society
Volume	57
Issue number	3
DOIs	https://doi.org/10.4134/BKMS.b190531
State	Published - 2020

Keywords

Gorenstein projective module
Projective module
PVMD

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title = "Finitely generated G-projective modules over PVMDS",

abstract = "Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ: M⊗RM* → HomR(HomR(M,M),R) is a surjective homomorphism. Particularly, if G-gldim(R) ≤ ∞ and Exti R(M,M) = 0 (i ≥ 1), then M is projective.",

keywords = "Gorenstein projective module, Projective module, PVMD",

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AB - Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ: M⊗RM* → HomR(HomR(M,M),R) is a surjective homomorphism. Particularly, if G-gldim(R) ≤ ∞ and Exti R(M,M) = 0 (i ≥ 1), then M is projective.

KW - Gorenstein projective module

KW - Projective module

KW - PVMD

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JO - Bulletin of the Korean Mathematical Society

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Finitely generated G-projective modules over PVMDS

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