Cohen–Macaulayness and sequentially Cohen–Macaulayness of monomial ideals
Hassan Noormohammadi
Azarbaijan Shahid Madani University, Tabriz, IranAhad Rahimi
Razi University, Kermanshah, Iran
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Abstract
In this paper, we give a characterization for Cohen–Macaulay rings where is a monomial ideal which satisfies bigsize = size . Next, we let be a polynomial ring and a monomial ideal. We study the sequentially Cohen–Macaulayness of with respect to . Moreover, if is a monomial ideal such that the associated prime ideals of are in pairwise disjoint sets of variables, a classification of to be sequentially Cohen–Macaulay is given. Finally, we compute grade where is a sequentially Cohen–Macaulay -module with respect to .
Cite this article
Hassan Noormohammadi, Ahad Rahimi, Cohen–Macaulayness and sequentially Cohen–Macaulayness of monomial ideals. Rend. Sem. Mat. Univ. Padova 140 (2018), pp. 221–236
DOI 10.4171/RSMUP/9