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

A congruence on ℕ n N^ n is an equivalence relation on ℕ n N^ n that is compatible with the
additive structure. If 𝕜\Bbbk is a field, and I is a binomial ideal in 𝕜 X 1,…, X n\Bbbk …

This chapter contains three major sections, each one roughly corresponding to a lecture.
The first section is on computing primary decompositions, the second one is more …

This is a book on combinatorial commutative algebra, more precisely, it describes some
applications of the combinatorics of monomial ideals to more general results in commutative …

A natural candidate for a generating set of the (necessarily prime) defining ideal of an n-
dimensional monomial curve, when the ideal is an almost complete intersection, is a full set …

To compute solutions of sparse polynomial systems efficiently we have to exploit the
structure of their Newton polytopes. While the application of polyhedral methods naturally …

The reason that this computation is easy is that we readily found the irreducible factors of the
polynomial x4− 1. In general, finding irreducible factors is a necessary prerequisite for the …