Cohen-Macaulay and (S 2 ) Properties of the Second Power of Squarefree Monomial Ideals

Do Trong Hoang, Giancarlo Rinaldo and Naoki Terai
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Do Trong Hoang: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam
Giancarlo Rinaldo: Department of Mathematics, University of Trento, via Sommarive, 14, 38123 Povo (Trento), Italy
Naoki Terai: Faculty of Education, Saga University, Saga 840-8502, Japan

Mathematics, 2019, vol. 7, issue 8, 1-8

Abstract: 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.

Keywords: Stanley-Reisner ideal; edge ideal; Cohen-Macaulay; (S2) condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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