Next Article in Journal
Fuzzy Counterparts of Fischer Diagonal Condition in ⊤-Convergence Spaces
Next Article in Special Issue
Cohen Macaulay Bipartite Graphs and Regular Element on the Powers of Bipartite Edge Ideals
Previous Article in Journal
Some (p, q)-Estimates of Hermite-Hadamard-Type Inequalities for Coordinated Convex and Quasi- Convex Functions
Previous Article in Special Issue
Compatible Algebras with Straightening Laws on Distributive Lattices
Article

Cohen-Macaulay and (S2) Properties of the Second Power of Squarefree Monomial Ideals

by 1,†, 2,† and 3,*,†
1
Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam
2
Department of Mathematics, University of Trento, via Sommarive, 14, 38123 Povo (Trento), Italy
3
Faculty of Education, Saga University, Saga 840-8502, Japan
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(8), 684; https://doi.org/10.3390/math7080684
Received: 16 June 2019 / Revised: 29 July 2019 / Accepted: 30 July 2019 / Published: 31 July 2019
(This article belongs to the Special Issue Current Trends on Monomial and Binomial Ideals)
We show that Cohen-Macaulay and (S 2 ) properties are equivalent for the second power of an edge ideal. We give an example of a Gorenstein squarefree monomial ideal I such that S / I 2 satisfies the Serre condition (S 2 ), but is not Cohen-Macaulay. View Full-Text
Keywords: Stanley-Reisner ideal; edge ideal; Cohen-Macaulay; (S2) condition Stanley-Reisner ideal; edge ideal; Cohen-Macaulay; (S2) condition
MDPI and ACS Style

Hoang, D.T.; Rinaldo, G.; Terai, N. Cohen-Macaulay and (S2) Properties of the Second Power of Squarefree Monomial Ideals. Mathematics 2019, 7, 684. https://doi.org/10.3390/math7080684

AMA Style

Hoang DT, Rinaldo G, Terai N. Cohen-Macaulay and (S2) Properties of the Second Power of Squarefree Monomial Ideals. Mathematics. 2019; 7(8):684. https://doi.org/10.3390/math7080684

Chicago/Turabian Style

Hoang, Do T., Giancarlo Rinaldo, and Naoki Terai. 2019. "Cohen-Macaulay and (S2) Properties of the Second Power of Squarefree Monomial Ideals" Mathematics 7, no. 8: 684. https://doi.org/10.3390/math7080684

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop