Jürgen Herzog, Somayeh Moradi, Masoomeh Rahimbeigi, Ali Soleyman Jahan: On the monomial reduction number of a monomial ideal in $K[x,y]$, 141-162

Abstract:

The reduction number of monomial ideals in the polynomial $K[x,y]$ is studied. We focus on ideals $I$ for which $J=(x^a,y^b)$ is a reduction ideal. The computation of the reduction number amounts to solve linear inequalities. In some special cases the reduction number can be explicitly computed.

Key Words: Monomial ideals, monomial reductions, reduction numbers, powers of monomial ideals.

2010 Mathematics Subject Classification: Primary 13F20; Secondary 13H10.