In the last two decades Cohen-Macaulay rings and modules have been central topics in
commutative algebra. This book meets the need for a thorough, self-contained introduction …

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

Historically, commutative algebra, whose foundations were laid by Dedekind, Hilbert,
Noether, and Krull, has developed in step with algebraic geometry, number theory …

Page 1 WINFRIED BRUNS JOSEPH GUBELADZE Polytopes, Rings, and K-Theory Springer
Springer Monographs in Mathematics Page 2 Springer Monographs in Mathematics For further …

Associated to any simplicial complex Δ on n vertices is a square-free monomial ideal IΔ in
the polynomial ring A= k [x1,…, xn], and its quotient k [Δ]= AI Δ known as the Stanley-Reisner …

Call a monomial ideal M" generic" if no variable appears with the same nonzero exponent in
two distinct monomial generators. Using a convex polytope first studied by Scarf, we obtain a …

This book contains the definitions of several ring constructions used in various applications.
The concept of a groupoid-graded ring includes many of these constructions as special …

A componentwise linear ideal is a graded ideal I of a polynomial ring such that, for each
degree q, the ideal generated by all homogeneous polynomials of degree q belonging to I …

This paper is devoted to the algebraic and combinatorial properties of polytopal semigroup
rings defined äs follows. Let P be a lattice polytope in IRn, ie a polytope whose vertices have …

Describing the properties of the minimal free resolution of a monomial ideal I is a difficult
problem posed in the early 1960's. The main directions of progress on this problem were:• …