Bulletin of the
Korean Mathematical Society BKMS

Let $(R,m)$ be a Cohen-Macaulay local ring and $I$ be an equimultiple ideal satisfying $I^2 = (a_1 ,\cdots, a_s ) I$ for some minimal reduction $a_1,\cdots,a_s$ of $I$, where $s = l(I)$. In this paper we shall prove that if $R/I$ is Cohen-Macaulay, then $gr_{I}(R)$ is Cohen-Macaulay.

Keywords: Cohen-Macaulay, equimultiple ideal, minimal reduction

MSC numbers: 13A30, 13H10