2007/12/21 by Marie A. Vitulli, Vitulli, Marie A.
Mathematics · #13A02 #13A30 #13F55 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #math.AG #msc:13A02 #msc:13A30 #msc:13F55
paper · pdf · doi:10.48550/arxiv.0712.3818
13 pages
arxiv created 2007/12/21 · openalex publication_date 2007/12/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we characterize the affine semigroup rings K[S] over an arbitrary field K that satisfy condition Rl of Serre. Our characterization is in terms of the face lattice of the positive cone pos(S) of S. We start by reviewing some basic facts about the faces of pos(S) and consequences for the monomial primes of K[S]. After proving our characterization we turn our attention to the Rees algebras of a special class of monomial ideals in a polynomial ring over a field. In this special case, some of the characterizing criteria are always satisfied. We give examples of nonnormal affine semigroup rings that satisfy R2.