ABSTRACT
In this chapter we study algebraic and geometric aspects of three important types of polynomial ideals and their quotient rings:
toric ideals ↪→ lattice ideals ↪→ binomial ideals. These ideals are interesting from a computational point of view and are
related to diverse fields, such as, numerical semigroups [173, 341], semigroup rings [180], commutative algebra and combinatorics [61, 317, 395], algebraic geometry [176, 317], linear algebra and polyhedral geometry [354, 420], integer programming [400], graph theory and combinatorial optimization [405], algebraic coding theory [348, 367], and algebraic statistics [142].
