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b-Filter Grade of an Ideal a for Triangulated Categories

Author

Listed:
  • Li Wang
  • Hailong Yao
  • Caihui Lan
  • Xuexia Dai

Abstract

Let a and b 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 T. We introduce the notion of the b-filter grade of a on X, denoted by f-gradb,a,X, and provide several characterizations and bounds for this invariant. In addition, we explore the relationships between f-gradb,a,X and two other invariants: the a-depth of X, written as depthRa,X, and the R-dimension of X, denoted by dimRX.

Suggested Citation

  • Li Wang & Hailong Yao & Caihui Lan & Xuexia Dai, 2026. "b-Filter Grade of an Ideal a for Triangulated Categories," Journal of Mathematics, Hindawi, vol. 2026, pages 1-9, January.
    • Handle: RePEc:hin:jjmath:2031854
    DOI: 10.1155/jom/2031854
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