Combinatorial commutative algebra is an active area of research with thriving connections to
other fields of pure and applied mathematics. This book provides a self-contained …

Homological algebra of modules over posets is developed, as closely parallel as possible to
that of finitely generated modules over noetherian commutative rings, in the direction of finite …

A theory of modules over posets is developed to define computationally feasible,
topologically interpretable data structures, in terms of birth and death of homology classes …

Primary decomposition of commutative monoid congruences is insensitive to certain
features of primary decomposition in commutative rings. These features are captured by the …

This survey of methods surrounding lattice point methods for binomial ideals begins with a
leisurely treatment of the geometric combinatorics of binomial primary decomposition. It then …

We extend the notion of standard pairs to the context of monomial ideals in semigroup rings.
Standard pairs can be used as a data structure to encode such monomial ideals, providing …

The commutative and homological algebra of modules over posets is developed, as closely
parallel as possible to the algebra of finitely generated modules over noetherian …

Interpreting the syzygy theorem for tame modules over posets in the setting of derived
categories of subanalytically constructible sheaves proves two conjectures due to …

Flat-injective presentations were introduced by Miller (2020) to provide combinatorial
descriptions of $\mathbb Z^ n $-graded modules. We consider them in the setting of local …

Let $ A $ be an integer $ d\times n $ matrix, and assume that the convex hull
$\operatorname {conv}(A) $ of its columns is a simplex of dimension $ d-1$ not containing …