Detecting the maximal-associated prime ideal of monomial ideals
Let \(I\subseteq R=k[x_1,\dots,x_n]\) be a monomial ideal. The present paper provides a neccessary and sufficient condition whether the graded maximal ideal of \(R\), \(\mathfrak{m}=\langle x_1,\dots,x_n\rangle\) is in the set of associated prime ideals of \(I\), \(\mathrm{Ass}_R(R/I)\). The main result of the paper, Theorem 2.7, yields a neccessary and sufficient condition as to whether \(\mathfrak{m}\in \mathrm{Ass}_R(R/I)\) solely using the elements of the unique minimal monomial generating set of \(I\)and without computing any minimal primary decomposition of \(I\).
scientific article; zbMATH DE number 7137969