Abstract
Let be two ideals of a commutative noetherian ring R. The concept of a -filter depth of on an arbitrary R-complex M, is introduced and several characterizations via Koszul complexes and local cohomology are given. Some bounds of for an R-complex such that are provided, in special cases, recover and generalize the known results about the usual (filter-) depth of modules.
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Acknowledgments
We sincerely thank the referee for his or her valuable suggestions and comments, and for pointing out some errors in the manuscript.