Rendiconti del Seminario Matematico della Università di Padova


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Volume 136, 2016, pp. 257–264
DOI: 10.4171/RSMUP/136-16

On the existence of Gorenstein projective precovers

Javad Asadollahi[1], Tahereh Dehghanpour[2] and Rasool Hafezi[3]

(1) Department of Mathematics, University of Isfahan, P.O.Box: 81746-73441, Isfahan, Iran
(2) Department of Mathematics, University of Isfahan, P.O. Box 81746-73441, Isfahan, Iran
(3) School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

We provide a simple proof for a recent result of Bravo, Gillespie and Hovey, showing that over a left coherent ring for which the projective dimension of at right modules is finite, the class of Gorenstein projective right modules is precovering. As an immediate application, we provide a description for the Gorenstein defect category over such rings.

Keywords: Precovering class, Gorenstein projective, Gorenstein flat

Asadollahi Javad, Dehghanpour Tahereh, Hafezi Rasool: On the existence of Gorenstein projective precovers. Rend. Sem. Mat. Univ. Padova 136 (2016), 257-264. doi: 10.4171/RSMUP/136-16