2018/06/22 by William Heinzer, Heinzer, William, K. Alan Loper +3
Mathematics · #13C05 #13E05 #13H15 #3A15 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1806.08736
openalex publication_date 2018/06/22 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Let D be a 2-dimensional regular local ring and let Q(D) denote the\nquadratic tree of 2-dimensional regular local overrings of D. We explore the\ntopology of the tree Q(D) and the family \R(D) of rings obtained\nas intersections of rings in Q(D). If A is a finite intersection of rings\nin Q(D), then A is Noetherian and the structure of A is well understood.\nHowever, other rings in \R(D) need not be Noetherian. The two main\ngoals of this paper are to examine topological properties of the quadratic tree\nQ(D), and to examine the structure of rings in the set \R(D).\n