Cohen–Macaulayness and sequentially Cohen–Macaulayness of monomial ideals

  • Hassan Noormohammadi

    Azarbaijan Shahid Madani University, Tabriz, Iran
  • Ahad Rahimi

    Razi University, Kermanshah, Iran

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