2005/11/02 by Jeffry Phan, Phan, Jeffry · 1 citation
Computer Science · Mathematics · #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.math/0511032
openalex publication_date 2005/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A minimal monomial ideal is the combinatorially simplest monomial ideal whose lcm-lattice equals a given finite atomic lattice L. The minimal ideal inherits many nice properties of any ideal I whose lcm-lattice also equals L, e.g. Cohen-Macaulayness and the dual property of having a linear resolution. Conversely, any ideal having a linear resolution is shown to be (essentially) minimal.