Regularity of ideals and their radicals

In this paper we compare the regularityreg I of a homogeneous idealI⊂K[x 1,...,x n] with that of its radical. We prove that regI ≥ reg\(\sqrt I\) ifR/I is a BuchsbaumR-module or ifI is a monomial ideal. We also prove the same result when\(\sqrt I\) defines a non-singular curve inP 3 under some additional hypotheses