On the depth of certain graded rings associated to an ideal

Abstract

Let (R,m) be a local ring and Ian ideal of R. In this work we find conditions on Ithat allow us to describe simple relations among depth R(It), depth gr_I(R), depth S(I) and depth S(I/I ²). These relations are useful also from a practical point, of view since it is usually difficult to evaluate depth gr_I(R) and depth S(I/I ²) even with the help of a computer. Furthermore we study the class of ideals that satisfy one of the required conditions and we show that ideals generated by quadratic sequences are in this class

The author was partially supported by a giant of CNR,Italy

The author was partially supported by a giant of CNR,Italy

Notes

The author was partially supported by a giant of CNR,Italy