## “School of Mathematics”

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Paper   IPM / M / 17188
 School of Mathematics Title: The saturation number of monomial ideals Author(s): Reza Abdolmaleki (Joint with A. A. Yazdan Pour) Status: To Appear Journal: Comm. Algebra Supported by: IPM
Abstract:
Let S = K[x_1, . . . , x_n] be the polynomial ring over a field K and m =(x1, . . . , xn) be the homogeneous maximal ideal of S. For an ideal I â S, let sat(I) be the minimum number k for which I:m^k = I:m^(k+1). In this paper, we compute the saturation number of irreducible monomial ideals and their powers. We apply this result to find the saturation number of the ordinary powers and symbolic powers of some families of monomial ideals in terms of the saturation number of irreducible components appearing in an irreducible decomposition of these ideals. Moreover, we give an explicit formula for the saturation number of monomial ideals in two variables.