Ideais de Ratliff- Rush

Abstract

In 1976, while studying some results on reduction, Louis J. Raltliff and David E. Rush introduced the following ideal e I = Sn=1(In+1 : In), at present known as Ratliff-Rush closure, in this work we present properties about such ideals, such as their asymptotic behavior, local-global type results and some pathologies of this closure. The main goal is to show the solution given by Amir Mafi, in 2017, to the question proposed by Maria E. Rossi and Irena Swanson, in 2003, on the Ratliff-Rush reduction number of an ideal I be less than or equal to the reduction number of I, being I an M-primary ideal in a Cohen-Macaulay local ring d-dimensional.