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.Comment: about 12 pages, LaTe

On the associated primes and the depth of the second power of squarefree monomial ideals

We present combinatorial characterizations for the associated primes of the second power of squarefree monomial ideals and criteria for this power to have positive depth or depth greater than one.Comment: To be published in Journal of Pure and Applied Algebr