Rendiconti del Seminario Matematico della Università di Padova


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

Published online: 2013-05-15

On Gorenstein Flat Preenvelopes of Complexes

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

(1) Lanzhou Jiatong University, Lanzhou (Gansu), China
(2) Northwest Normal University, Lanzhou (Gansu), China
(3) Lanzhou Jiatong University, 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