Regularity, a*-Invariant and the Associated Graded Module to a Filtration

Abstract

Let T be a graded module over a positively graded algebra. We prove that reg _k+1(T) = max {reg _k (T/zT) − d + 1, end(0: _T g)} and for any filter regular element z of degree d with respect to T. From this result, we obtain some generalizations of some known results. In addition, we discuss behavior of regularity and a*-invariant of the graded module associated to a filtration when it has large depth.

Key Words:

• Associated graded module
• Filtration
• Filter-regular
• a*-Invariant
• Local cohomology
• Regularity

2000 Mathematics Subject Classification:

• Primary 13D45
• Secondary 13A02

ACKNOWLEDGMENTS

Thank the referee very much for his/her careful reading.

This research is partially supported by National Natural Science Foundation of China (No. 10671122) and Collegial Natural Science Research Program of Education Department of Jiangsu Province (No. 09KJB110006).

Notes

Communicated by S. Goto.