Combinatorial commutative algebra is a new branch in the modern research of mathematics. It has recently developed by combining different techniques used in commutative algebra and in combinatorics. Monomial ideals are at the intersection of commutative algebra and combinatorics. The radical monomial ideals which are ideals generated by squarefree monomials, have a beautiful combinatorial interpretation in terms of simplicial complexes. With any simplicial complex one may associate a squarefree monomial ideal and viceversa. By this process, the combinatorial properties of the simplicial...