Articles written in Proceedings – Mathematical Sciences
Volume 120 Issue 2 April 2010 pp 163-168
The aim of this paper is to study homological properties of deficiently extremal Cohen–Macaulay algebras. Eagon–Reiner showed that the Stanley–Reisner ring of a simplicial complex has a linear resolution if and only if the Alexander dual of the simplicial complex is Cohen–Macaulay. An extension of a special case of Eagon–Reiner theorem is obtained for deficiently extremal Cohen–Macaulay Stanley–Reisner rings.
Volume 121 Issue 3 August 2011 pp 259-265
The aim of this article is to study the homological properties of deficiently extremal Gorenstein algebras. We prove that if $R/I$ is an odd deficiently extremal Gorenstein algebra with pure minimal free resolution, then the codimension of $R/I$ must be odd. As an application, the structure of pure minimal free resolution of a nearly extremal Gorenstein algebra is obtained.
Volume 130 All articles Published: 6 August 2020 Article ID 0048 Article
To every finite simple graph $G$, we associate the so-called edge ideal $I (G)$, which is a square-free quadratic monomial ideal generated by the monomials corresponding to the edges of $G$. In this paper, we determine all the initial graded Betti numbers of edge ideals of triangular graphs and alternate triangular graphs in terms of the underlying graph. We also compute the regularity of edge ideals of triangular and alternate triangular graphs.
Volume 130, 2020
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