This paper introduces the notion of depth with respect to ideals for unbounded DG-modules,and gives a reduction formula and the local nature of this depth.As applications,we provide several bounds of the depth in spec...This paper introduces the notion of depth with respect to ideals for unbounded DG-modules,and gives a reduction formula and the local nature of this depth.As applications,we provide several bounds of the depth in special cases,and recover and generalize the known results about the depth of complexes.In addition,the width with respect to ideals for unbounded DG-modules is investigated and the depth and width formulas for DG-modules are generalized.展开更多
基金supported by National Natural Science Foundation of China(11761060,11901463,12061061)Science and Technology project of Gansu province(20JR5RA517)+1 种基金Innovation Ability Enhancement Project of Gansu Higher Education Institutions(2019A-002)Improvement of Young Teachers’Scientific Research Ability(NWNU-LKQN-18-30).
文摘This paper introduces the notion of depth with respect to ideals for unbounded DG-modules,and gives a reduction formula and the local nature of this depth.As applications,we provide several bounds of the depth in special cases,and recover and generalize the known results about the depth of complexes.In addition,the width with respect to ideals for unbounded DG-modules is investigated and the depth and width formulas for DG-modules are generalized.
