Cohen–Macaulayness and sequentially Cohen–Macaulayness of monomial ideals
Rendiconti del Seminario Matematico della Università di Padova, Tome 140 (2018), pp. 221-236.

In this paper, we give a characterization for Cohen–Macaulay rings R/I where IR=K[y 1 ,,y n ] is a monomial ideal which satisfies bigsize I = size I. Next, we let S=K[x 1 ,...,x m ,y 1 ,...,y n ] be a polynomial ring and IS a monomial ideal. We study the sequentially Cohen–Macaulayness of S/I with respect to Q=(y 1 ,...,y n ). Moreover, if IR 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.

Publié le :
DOI : 10.4171/RSMUP/9
Classification : 13, 11
Mots clés : Monomial ideals, Cohen–Macaulay, sequentially Cohen–Macaulay, size of an ideal
Noormohammadi, Hassan 1 ; Rahimi, Ahad 2

1 Azarbaijan Shahid Madani University, Tabriz, Iran
2 Razi University, Kermanshah, Iran
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     author = {Noormohammadi, Hassan and Rahimi, Ahad},
     title = {Cohen{\textendash}Macaulayness and sequentially {Cohen{\textendash}Macaulayness} of monomial ideals},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {221--236},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {140},
     year = {2018},
     doi = {10.4171/RSMUP/9},
     mrnumber = {3880218},
     zbl = {1429.13012},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/9/}
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Noormohammadi, Hassan; Rahimi, Ahad. Cohen–Macaulayness and sequentially Cohen–Macaulayness of monomial ideals. Rendiconti del Seminario Matematico della Università di Padova, Tome 140 (2018), pp. 221-236. doi : 10.4171/RSMUP/9. http://www.numdam.org/articles/10.4171/RSMUP/9/

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