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.
2000 Mathematics Subject Classification:
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.