2025/04/15 by Jason G. Boynton, Boynton, Jason, Jim Coykendall +4 · 1 citation
Mathematics · #13A05 #13B22 #13F15 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2504.11394
openalex publication_date 2025/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The behavior of factorization properties in various ring extensions is a central theme in commutative algebra. Classically, the UFDs are (completely) integrally closed and tend to behave well in standard ring extensions, with the notable exception of power series extension. The half-factorial property is not as robust; HFDs need not be integrally closed and the half-factorial property is not necessarily preserved in integral extensions or even localizations. Here we exhibit classes of HFDs that behave well in (almost) integral extensions, resolve an open question on the behavior of the boundary map, and give a squeeze theorem for elasticity in certain domains.