**Local Cohomology of Multi-Rees Algebras with Applications to joint Reductions and Complete Ideals **

* Shreedevi K. Masuti, Tony J. Puthenpurakal, J. K. Verma *

**Abstract**

Let *d* and **I**=(*I* _{1},…,*I* _{ d }) be *R*. We prove that **I**−admissible filtration and (*x* _{ i j }) is a strict complete reduction of *I*,*J*,*K* is zero in an analytically unramified Cohen-Macaulay local ring of dimension 3 if and only if