TY - JOUR
T1 - GORENSTEIN PROJECTIVE PRECOVERS AND FINITELY PRESENTED MODULES
AU - Estrada, Sergio
AU - Iacob, Alina
N1 - Publisher Copyright:
© Rocky Mountain Mathematics Consortium.
PY - 2024/6
Y1 - 2024/6
N2 - The existence of the Gorenstein projective precovers over arbitrary rings is an open question. It is known that if the ring has finite Gorenstein global dimension, then every module has a Gorenstein projective precover. We prove here a “reduction” property — we show that, over any ring, it suffices to consider finitely presented modules: if there exists a nonnegative integer n such that every finitely presented module has Gorenstein projective dimension ≤ n, then the class of Gorenstein projective modules is special precovering.
AB - The existence of the Gorenstein projective precovers over arbitrary rings is an open question. It is known that if the ring has finite Gorenstein global dimension, then every module has a Gorenstein projective precover. We prove here a “reduction” property — we show that, over any ring, it suffices to consider finitely presented modules: if there exists a nonnegative integer n such that every finitely presented module has Gorenstein projective dimension ≤ n, then the class of Gorenstein projective modules is special precovering.
KW - finitely presented modules
KW - Gorenstein projective dimension
KW - Gorenstein projective precover
UR - http://www.scopus.com/inward/record.url?scp=85200264268&partnerID=8YFLogxK
U2 - 10.1216/rmj.2024.54.715
DO - 10.1216/rmj.2024.54.715
M3 - Article
AN - SCOPUS:85200264268
SN - 0035-7596
VL - 54
SP - 715
EP - 721
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
IS - 3
ER -