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 $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, \cdots, x_{i_l}^{a_l})$.
Yang, S., Chu, L., & Qian, Y. (2015). Castelnuovo-Mumford regularity of products of monomial ideals. Journal of Algebra and Related Topics, 3(2), 53-59.
MLA
S. Yang; L. Chu; Y. Qian. "Castelnuovo-Mumford regularity of products of monomial ideals". Journal of Algebra and Related Topics, 3, 2, 2015, 53-59.
HARVARD
Yang, S., Chu, L., Qian, Y. (2015). 'Castelnuovo-Mumford regularity of products of monomial ideals', Journal of Algebra and Related Topics, 3(2), pp. 53-59.
VANCOUVER
Yang, S., Chu, L., Qian, Y. Castelnuovo-Mumford regularity of products of monomial ideals. Journal of Algebra and Related Topics, 2015; 3(2): 53-59.
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