Media Summary: We begin to study initial ideals and initial complexes of lattice ideals. We describe the initial ideal of a lattice ideal in terms of an optimization problem in integer programming. We also describe the ... We show that a semigroup has a unique minimal set of generators. For saturated semigroups this is called the Hilbert basis.
Lecture 39 Combinatorial Commutative Algebra - Detailed Analysis & Overview
We begin to study initial ideals and initial complexes of lattice ideals. We describe the initial ideal of a lattice ideal in terms of an optimization problem in integer programming. We also describe the ... We show that a semigroup has a unique minimal set of generators. For saturated semigroups this is called the Hilbert basis. We prove that a semi group ring fa isomorphic to the quotient of the polynomial ring by the lattice ideal, and offer several ... Uded here and showing you that e is irrational turns out to be possible with just the information that you know from college Commutative algebra in solving differential equations - Part I by Prof. Debasattam Pal
We discuss polytopes, polyhedral complexes, and their chain complexes. We begin to discuss semigroup algebras and lattice ideals. I describe term orders and Gröbner bases in a free module F over a polynomial ring. I state and begin to prove that if $G$ is a ... We discuss the hull resolution, a cellular resolution of an arbitrary monomial ideal inn variables which has length at most $n$.
