1999/09/28 by Diane Maclagan, Maclagan, Diane
Mathematics · #13P10 (Primary) 06A06 #52B20 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.AG #math.CO #msc:06A06 #msc:13P10 #msc:52B20
paper · pdf · doi:10.48550/arxiv.math/9909168
8 pages
arxiv created 1999/09/28 · openalex publication_date 1999/09/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main result of this paper is that all antichains are finite in the poset of monomial ideals in a polynomial ring, ordered by inclusion. We present several corollaries of this result, both simpler proofs of results already in the literature and new results. One natural generalization to more abstract posets is shown to be false.