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.
Keywords:
Acknowledgments
We sincerely thank the referee for his or her valuable suggestions and comments, and for pointing out some errors in the manuscript.