Cohen-Macaulayness and sequentially Cohen-Macaulayness of monomial ideals (Q2414668)

Summary: In this paper, we give a characterization for Cohen-Macaulay rings \(R/I\) where \(I\subset R=K[y_1, \dots, y_n]\) is a monomial ideal which satisfies bigsize \(I\) = size \(I\). Next, we let \(S=K[x_1,\ldots,x_m, y_1,\ldots,y_n]\) be a polynomial ring and \(I\subset S\) a monomial ideal. We study the sequentially Cohen-Macaulayness of \(S/I\) with respect to \(Q=(y_1,\ldots,y_n)\). Moreover, if \(I\subset R\) is a monomial ideal such that the associated prime ideals of \(I\) are in pairwise disjoint sets of variables, a classification of \(R/I\) to be sequentially Cohen-Macaulay is given. Finally, we compute grade$(Q, M)\) where \(M\) is a sequentially Cohen-Macaulay \(S\)-module with respect to \(Q\).