[1] Zeng Yuedi, Chen Jianlong,. On Gorenstein FP-injective modules [J]. Journal of Southeast University (English Edition), 2011, 27 (1): 115-118. [doi:10.3969/j.issn.1003-7985.2011.01.024]

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On Gorenstein FP-injective modules()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

27

Issue:

2011 1

Page:

115-118

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2011-03-30

Info

Title:

On Gorenstein FP-injective modules

Author(s):

Zeng Yuedi;  Chen Jianlong

Department of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

coherent ring;  Gorenstein FP-injective dimension;  Gorenstein FP-injective precover;  Gorenstein FP-injective preenvelope

PACS:

O153.39

DOI:

10.3969/j.issn.1003-7985.2011.01.024

Abstract:

An R-module M is called Gorenstein FP-injective if there is an exact sequence …→E₁→E₀→E⁰→E¹→… of FP-injective R-modules with M=ker(E⁰→E¹)and such that Hom(E, -)leaves the sequence exact whenever E is an FP-injective R-module. Some properties of Gorenstein FP-injective are obtained. Moreover, it is proved that a ring is left Noetherian if and only if every Gorenstein FP-injective left R-module is Gorenstein injective. Furthermore, it is shown that over an n-FC and perfect ring R, a left R-module M is Gorenstein FP-injective if and only if M≅F⊕H for some FP-injective left R-module F and some strongly Gorenstein FP-injective R-module H. In view of this, Gorenstein FP-injective precovers and Gorenstein FP-injective preenvelopes are considered.

References:

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Memo

Memo:

Biographies: Zeng Yuedi(1983—), female, graduate; Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.10971024), Specialized Research Fund for the Doctoral Program of Higher Education(No.200802860024).
Citation: Zeng Yuedi, Chen Jianlong. On Gorenstein FP-injective modules[J].Journal of Southeast University(English Edition), 2011, 27(1):115-118.[doi:10.3969/j.issn.1003-7985.2011.01.024]

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