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STRONGLY GORENSTEIN FLAT MODULES

Part of: Modules, bimodules and ideals Homological algebra

Published online by Cambridge University Press:  01 June 2009

NANQING DING ,
YUANLIN LI  and
LIXIN MAO
NANQING DING*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, PR China (email: [email protected])
YUANLIN LI
Affiliation:
Department of Mathematics, Brock University, St. Catharines, Ontario, Canada L2S 3A1 (email: [email protected])
LIXIN MAO
Affiliation:
Institute of Mathematics, Nanjing Institute of Technology, Nanjing 211167, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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In this paper, strongly Gorenstein flat modules are introduced and investigated. An R-module M is called strongly Gorenstein flat if there is an exact sequence ⋯→P1→P0→P0→P1→⋯ of projective R-modules with M=ker (P0→P1) such that Hom(−,F) leaves the sequence exact whenever F is a flat R-module. Several well-known classes of rings are characterized in terms of strongly Gorenstein flat modules. Some examples are given to show that strongly Gorenstein flat modules over coherent rings lie strictly between projective modules and Gorenstein flat modules. The strongly Gorenstein flat dimension and the existence of strongly Gorenstein flat precovers and pre-envelopes are also studied.

Keywords

strongly Gorenstein flat moduleGorenstein flat moduleprecoverpre-envelopecotorsion theory

MSC classification

Secondary: 16D40: Free, projective, and flat modules and ideals 18G20: Homological dimension
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 3 , June 2009 , pp. 323 - 338
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This research was partially supported by SRFDP (No. 20050284015), NSFC (No. 10771096), a discovery grant from NSERC, Science Research Fund of Nanjing Institute of Technology (KXJ07061), Jiangsu 333 Project, and Jiangsu Qinglan Project.

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