Seminar Algebra & Geometry: Thomas Kahle
Thomas Kahle, ETH Zürich
How primary decomposition of monoid congruences and binomial ideals is wrong.
In a polynomial ring, a binomial says that two monomials are scalar multiples of each other. Forgetting about the scalars, a binomial ideal describes an equivalence relation on the monoid of exponents.
Ideally one would want to carry out algebraic computations, such as primary decomposition of binomial ideals, entirely in this combinatorial language. We will present such a calculus, enabling one to compute by looking at pictures of monoids.