Rendiconti del Seminario Matematico della Università di Padova


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Volume 129, 2013, pp. 171–187
DOI: 10.4171/RSMUP/129-10

On Gorenstein Flat Preenvelopes of Complexes

Gang Yang[1], Zhongkui Liu[2] and Li Liang[3]

(1) Department of Mathematics, Lanzhou Jiatong University, 730070, Lanzhou, Gansu, China
(2) Department of Mathematics, Northwest Normal University, 730070, Lanzhou, Gansu, China
(3) Department of Mathematics, Lanzhou Jiatong University, 730070, Lanzhou, Gansu, China

In this paper we show that if the class ${\cal B}$ of $R$-modules is closed under well ordered direct limits, then the class ${\cal B}$ is preenveloping in the category of $R$-modules if and only if the class $dw{\cal B}$ is preenveloping in the category of $R$-complexes, where $dw{\cal B}$ denotes the class of all complexes with all components in ${\cal B}$. As an immediate consequence, we get that over commutative and Noetherian rings with dualizing complexes every complex admits a Gorenstein flat preenvelope.

Keywords: (pre)envelopes, Gorenstein injective modules (complexes), FP-injective modules, Gorenstein flat modules (complexes)

Yang Gang, Liu Zhongkui, Liang Li: On Gorenstein Flat Preenvelopes of Complexes. Rend. Sem. Mat. Univ. Padova 129 (2013), 171-187. doi: 10.4171/RSMUP/129-10