The main purpose of this book is to introduce algebraic, combinatorial, and computational
methods to study monomial algebras and their presentation ideals, including Stanley …

This volume contains the proceedings of the Workshop in Commutative Algebra, held at
Salvador (Brazil) on August 8-17, 1988. A few invited papers were included which were not …

We give formulas, in terms of graph theoretical invariants, for the minimum distance and the
generalized Hamming weights of the linear code generated by the rows of the incidence …

Cremona maps defined by monomials of degree 2 are thoroughly analyzed and classified
via integer arithmetic and graph combinatorics. In particular, the structure of the inverse map …

Consider an ideal I⊂ K [x 1,…, xn], with K an arbitrary field, generated by monomials of
degree two. Assuming that I does not have a linear resolution, we determine the step s of the …

Let be the toric ideal of a homogeneous normal configuration. We prove that is generated by
circuits if and only if each unbalanced circuit of has a connector which is a linear …

Given a standard graded polynomial ring R= k [x1,…, xn] over a field k of characteristic zero
and a graded k-subalgebra A= k [f1,…, fm]⊂ R, one relates the module ΩA/k of Kähler k …

For any graph, one can construct a ring, called the edge ring, which is a quadratic-monomial
generated subring of the Laurent polynomial ring $ k [x_1^{\pm 1},\dots, x_n^{\pm 1}] $. In …

Esta tesis se centra en el estudio de los números de Betti graduados y otros invariantes
homológicos como la regularidad de Castelnuovo-Mumford o la dimensión proyectiva …

Determining whether an arbitrary subring $ R $ of $ k [x_1^{\pm 1},\dots, x_n^{\pm 1}] $ is a
normal domain is, in general, a nontrivial problem, even in the special case of a monomial …