Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2010; 47(4): 691-704

Printed July 1, 2010

https://doi.org/10.4134/JKMS.2010.47.4.691

Copyright © The Korean Mathematical Society.

Gorenstein-injectors, Gorenstein-flators

Qinqin Gu, Xiaosheng Zhu, and Wenping Zhou

Anhui University of Technology, Nanjing University, Anhui University of Technology

Abstract

Over a ring $R$, let $P_{R}$ be a finitely generated projective right $R$-module. Then we define the $G$-injector ($G$-projector) if $P_{R}$ preservers Gorenstein injective modules (Gorenstein projective modules), the $G$-flator if $P_{R}$ preservers Gorenstein flat modules. $G$-injector ($G$-flator) and $G$-injector are characterized focus primarily on the cases where $R$ is a Gorenstein ring, and under this condition we also study the relations between the injector (projector, flator) and the $G$-injector ($G$-projector, $G$-flator). Over any ring we also give the characteristics of $G$-injector ($G$-flator) by the Gorenstein injective (Gorenstein flat) dimensions of modules.

Keywords: Gorenstein-injector, perfect Gorenstein-injector, Gorenstein-flator, perfect Gorenstein-flator

MSC numbers: 13D05, 13D02, 16E10, 16E30

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