Results on the Hilbert coefficients and reduction numbers

Let $(R,\mathfrak{m})$ be a $d$-dimensional Cohen-Macaulay local ring, $I$ an $\mathfrak{m}$-primary ideal and $J$ a minimal reduction of $I$. In this paper we study the independence of reduction ideals and the behavior of the higher Hilbert coefficients. In addition, we give some examples in this regards.