Algebraical Properties Of Powers Of Monomial Ideals

Our paper is divided into five chapters. In the first and second chapters, we give an outline and some backgrounds of this paper.Let G be a simple graph and I be its edge ideal. It was shown in [9] that Ass(R/I) c Ass(R/I2) c Ass(R/I3) c. we give a much simpler proof for this result in Chapter 3.In the fourth chapter, we investigate when Ass(R/Il) stabilize in the case that Iis the edge ideal of some graph G. In a particular case when G is a connected graph containing a unique odd cycle, we solve the question completely.Let I be a square-free monomial ideal. We prove in the fifth chapter that if I is normally torsion-free then all the minors of I are normally torsion-free as well, and consequently,I satisfies the packing property.