A Study of Strongly Cohen–Macaulay Ideals by Delta Invariant

Abstract

Let R be a Cohen–Macaulay local ring, I a strongly Cohen–Macaulay ideal of R. We show that $$R/\text{ Ann }\,_R(I)$$ is a maximal Cohen–Macaulay R-module by means of the delta-invariant. Also it is shown that there exists a Cohen–Macaulay ideal J of R such that the $$\delta _{R/J}$$ -invariant of all Koszul homologies of R with respect I is zero.