Castelnuovo-Mumford regularity of products of monomial ideals

Document Type: Research Paper


Soochow University


Let $R=k[x_1,x_2,\cdots, x_N]$ be a polynomial ring over a field $k$. We prove that for any positive integers $m, n$, $\text{reg}(I^mJ^nK)\leq m\text{reg}(I)+n\text{reg}(J)+\text{reg}(K)$ if $I, J, K\subseteq R$ are three monomial complete intersections ($I$, $J$, $K$ are not necessarily proper ideals of the polynomial ring $R$), and $I, J$ are of the form $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, \cdots, x_{i_l}^{a_l})$.