Freiman ideals and the number of generators of powers of monomial ideals

Abstract

Let denote the number of generators of a monomial ideal I. It is well known that for In this paper we construct monomial ideals I in such that for all given any positive integer l. Also, we extend some results of Eliahou et al. by constructing monomial ideals in with and investigate for monomial ideals in R. Furthermore, we generalize the definition of Freiman ideals given in Herzog and Zhu and extend some results with simpler proofs. In particular, we give a complete characterization of Freiman ideals of maximum height in R.