Abstract
Let (R, 𝔪) be a Noetherian local ring and M a finitely generated R -module. The two notions of generalized regular sequence and generalized depth are introduced as extensions of the known notions of regular sequence and depth, respectively. Some properties of generalized regular sequence and generalized depth, which are closely related to those of regular sequence and depth, are given. If x1 ,…, xr is a generalized regular sequence of M , then
ACKNOWLEDGMENT
I am grateful to Professor N. T. Cuong for useful suggestion. I thank the referee for helpful comments, and the ICTP, Trieste, Italy, for the financial support.
Notes
#Communicated by I. Swanson.