Subalgebras of the Stanley - Reisner Ring

On a special class of Stanley-Reisner ideals

For an $n$-gon with vertices at points $1,2,cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the $S$-module $S/I$ where  $S=K[x_{1},cdots, x_{n}]$ and $I$ is the associated ideal to ...

On Isomorphism of Simplicial Complexes and Their Related Algebras

The Complement of a D-Tree is Pure Shellable

Addendum to ”frobenius and Cartier Algebras of Stanley-reisner

We give a purely combinatorial characterization of complete Stanley-Reisner rings having a principally generated (equivalently, finitely generated) Cartier algebra.

Stanley–reisner Rings with Large Multiplicities Are Cohen–macaulay

We prove that certain class of Stanley–Reisner rings having sufficiently large multiplicities are Cohen–Macaulay using Alexander duality.