On the Normality of One-fibered Monomial Ideals

This paper presents a generalization to the higher-dimensional situation of the main results of the first author about the normality of one-fibered monomial ideals [2, Theoremes 2.4 and 3.8]. Precisely, we show that if I is a monomial ideal of R = k[x(1), x(2),...,x(d)], then I is normal one-fibered if and only if for all positive integers n and all x, y in R such that xy is an element of I-2n, either x or y belongs to I-n.