JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (10): 18-23.doi: 10.6040/j.issn.1671-9352.0.2016.574

Previous Articles     Next Articles

Homology resolutions and homological dimensions of complexes

MA Xin, ZHAO You-yi*, NIU Xue-na   

  1. Colleage of Science, Gansu Agricultural University, Lanzhou 730070, Gansu, China
  • Received:2016-12-05 Online:2017-10-20 Published:2017-10-12

PDF (PC)

474

Abstract: The existence of homology resolutions of bounded above complexes in the relative case has been aprroved, which was the generalization of the usual homology resolutions. Then we define relatived homological dimensions of bounded above complexes and gave an equivalent characterization.

Key words: dgX resolution, right X-approximation, homological dimensions

CLC Number: 

  • O153.3
[1] SPALTENSTEIN N. Resolutions of unbounded complexes[J]. Compositio Mathematica, 1988, 65(2):121-154.
[2] GAO N, ZHANG P. Gorenstein derived categories[J]. Journal of Algebra, 2010, 323(7):2041-2057.
[3] REN Wei, LIU Zhongkui, YANG Gang. Derived categories with respect to Ding modules[J]. Journal of Algebra and Its Applications, 2013, 12(6):14.
[4] BELIGIANNIS A. The homological theory of contravariantly finite subcategories: auslander-buchweitz contexts, gorenstein categories and(co-)stabilization[J]. Communications in Algebra, 2000, 28(10):4547-4596.
[5] CHEN Xiaowu. Homotopy Equivalences induced by Balanced Pairs[J]. Journal of Algebra, 2008, 324(10):2718-2731.
[6] ASADOLLAHI J, BAHIRAEI P, HAFEZI R, et al. On relative derived categories[J]. Mathematics, 2013: 5455-5477.
[7] ZHANG Pu. Triangulated categories and derived categories[M]. Beijing: Science Press, 2015.
[1] CHEN Xiu-li, CHEN Jian-long. Homological dimensions with respect to semidualizing modules and excellent extensions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 85-89.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd