Let and be two homogeneous ideals in a graded‐commutative Noetherian ring R , and let X be an object in a compactly generated R ‐linear triangulated category . We introduce the notion of the ‐filter grade of on X , denoted by f‐, and provide several characterizations and bounds for this invariant. In addition, we explore the relationships between f‐ and two other invariants: the ‐depth of X , written as , and the R ‐dimension of X , denoted by dim R X .
Wang et al. (Thu,) studied this question.
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