Given the monomial ideal I=(x_1^{ { \alpha}_1},...,x_{ n}^{ { \alpha}_{ n}})\subset K[x_1,...,x_{ n}] where { \alpha}_{ i} are positive integers and K a field and let J be the integral closure of I . It is a challenging problem to translate the question of the normality of J into a question about the exponent set { \Gamma}(J) and the Newton polyhedron NP(J). A relaxed version of this problem is to give necessary or sufficient conditions on { \alpha}_1,...,{ \alpha}_{ n} for the normality of J. We show that if { \alpha}_{ i}\epsilon{ s,l} with s and l arbitrary positive integers, then J is normal.
Categories: math.AC