TY - JOUR
T1 - A refinement of Gorenstein flat dimension via the flat–cotorsion theory
AU - Christensen, Lars Winther
AU - Estrada, Sergio
AU - Liang, Li
AU - Thompson, Peder
AU - Wu, Dejun
AU - Yang, Gang
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2021/2/1
Y1 - 2021/2/1
N2 - We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the Gorenstein flat dimension, behaves as one expects of a homological dimension without extra assumptions on the ring. Crucially, we show that it coincides with the Gorenstein flat dimension for complexes where the latter is finite, and for complexes over right coherent rings—the setting where the Gorenstein flat dimension is known to behave as expected.
AB - We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the Gorenstein flat dimension, behaves as one expects of a homological dimension without extra assumptions on the ring. Crucially, we show that it coincides with the Gorenstein flat dimension for complexes where the latter is finite, and for complexes over right coherent rings—the setting where the Gorenstein flat dimension is known to behave as expected.
KW - Flat-cotorsion module
KW - Gorenstein flat dimension
KW - Gorenstein flat-cotorsion dimension
UR - http://www.scopus.com/inward/record.url?scp=85091935910&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2020.09.024
DO - 10.1016/j.jalgebra.2020.09.024
M3 - Article
AN - SCOPUS:85091935910
VL - 567
SP - 346
EP - 370
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -