Media Summary: We prove that a semi group ring fa isomorphic to the quotient of the polynomial ring by the lattice ideal, and offer several ... We show that a semigroup has a unique minimal set of generators. For saturated semigroups this is called the Hilbert basis. We describe the initial ideal of a lattice ideal in terms of an optimization problem in integer programming. We also describe the ...
Lecture 37 Combinatorial Commutative Algebra - Detailed Analysis & Overview
We prove that a semi group ring fa isomorphic to the quotient of the polynomial ring by the lattice ideal, and offer several ... We show that a semigroup has a unique minimal set of generators. For saturated semigroups this is called the Hilbert basis. We describe the initial ideal of a lattice ideal in terms of an optimization problem in integer programming. We also describe the ... Every monomial ideal I in n variables has a cellular resolution by a simplicial complex, of length at most n. When I is generic, the ... We begin to study initial ideals and initial complexes of lattice ideals. We begin by discussing how to view hull complexes for artinian monomial ideals. Then we discuss generic monomial ideals.
Sara Faridi, Dalhousie University Wednesday, June 4th, 2025 ... We show how the Betti numbers of a monomial ideal can be obtained from a cellular resolution.
