Let a \subseteq \mathbb{C} [x1, ..., xn] be a monomial ideal andJ(a^{c}) the multiplier ideal of a with coefficient c. Then J(a^{c}) is also a monomial ideal of \mathbb{C} [x1, ..., xn], and the equality J(a^{c}) = a implies that 0 < c < n + 1. We mainly discuss the problem when J (a) = a or J({a^{n = 1 - \varepsilon }}) = a for all 0 < ε < 1. It is proved that if J (a) = a then a is principal, and if J({a^{n = 1 - \varepsilon }}) = a holds for all 0 < ε < 1 then a = (x1, ..., xn). One global result is also obtained. Let ã be the ideal sheaf on \mathbb{P}^{n-1} associated with a. Then it is proved that the equality J (ã) = ã implies that ã is principal., Cheng Gong, Zhongming Tang., and Obsahuje seznam literatury