LetGbe a graph on the vertex setV, andR = k[V] a polynomial ring over a fieldk. We give a very explicit description of the integral closure of the monomial subringk[G] ⊂ R, generated by the squarefree monomials of degree ...

For a finitely generated module E over the Noetherian ring R we consider formulas for the Krull dimension of the symmetric algebra S(E). A result of Huneke and Rossi is re-proved and an eiffective formulais derived that ...

We study algebras defined by finite sets G = {M1, ..., Mq} of monomials of a polynomial ring R. There are two basic algebras: (i) k[G] = k[M1, ..., Mq], the k-subalgebra of R spanned by the Mi, and (ii) the quotient ring ...