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 - Funding Information:
L.W.C. was partly supported by Simons Foundation collaboration grant 428308 ; S.E. was partly supported by grant MTM2016-77445-P ( AEI/FEDER,UE ) and Fundación Seneca grant 19880/GERM/15 ; L.L. was partly supported by NSF of China grants 11761045 and 11971388 , and NSF of Gansu Province grant 18JR3RA113 ; D.W. was partly supported by NSF of China grants 11761047 and 11861043 ; G.Y. was partly supported by NSF of China grant 11561039 ; both L.L. and G.Y. were also partly supported by the Foundation of A Hundred Youth Talents Training Program of Lanzhou Jiaotong University . The research was partly done during D.W.'s year-long visit to Texas Tech University; the hospitality of the TTU Department of Mathematics and Statistics is acknowledged with gratitude.
Funding Information:
L.W.C. was partly supported by Simons Foundation collaboration grant 428308; S.E. was partly supported by grant MTM2016-77445-P (AEI/FEDER,UE) and Fundaci?n Seneca grant 19880/GERM/15; L.L. was partly supported by NSF of China grants 11761045 and 11971388, and NSF of Gansu Province grant 18JR3RA113; D.W. was partly supported by NSF of China grants 11761047 and 11861043; G.Y. was partly supported by NSF of China grant 11561039; both L.L. and G.Y. were also partly supported by the Foundation of A Hundred Youth Talents Training Program of Lanzhou Jiaotong University. The research was partly done during D.W.'s year-long visit to Texas Tech University; the hospitality of the TTU Department of Mathematics and Statistics is acknowledged with gratitude.
Publisher Copyright:
© 2020 Elsevier Inc.
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 -