ON THE DEPTH OF CERTAIN GRADED RINGS ASSOCIATED TO AN IDEAL

Let (R, m) be a local ring and I an ideal of R. In this work we find c onditions on I that 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 dif ficult to evaluate depth gr(I)(R) and depth S(I/I-2) even with the hel p of a computer. Furthermore we study the class of ideals that satisfy one of the required conditions and we show that ideals generated by q uadratic sequences are in this class.