Results 11 to 20 of about 2,005,027 (257)
K -theory of valuation rings [PDF]
Compositio Mathematica, 2021 We prove several results showing that the algebraic $K$ -theory of valuation rings behaves as though such rings were regular Noetherian, in particular an analogue of the ...
Kelly, Shane, Morrow, Matthew
semanticscholar +5 more sources
DEFINABLE HENSELIAN VALUATION RINGS [PDF]
The Journal of Symbolic Logic, 2015 AbstractWe give model theoretic criteria for the existence of ∃∀ and ∀∃- formulas in the ring language to define uniformly the valuation rings ${\cal O}$ of models $\left( {K,\,{\cal O}} \right)$ of an elementary theory Σ of henselian valued fields. As one of the applications we obtain the existence of an ∃∀-formula defining uniformly the valuation ...
A. Prestel
semanticscholar +7 more sources
Characterizing diophantine henselian valuation rings and valuation ideals [PDF]
, 2016 We give a characterization, in terms of the residue field, of those henselian valuation rings and those henselian valuation ideals that are diophantine. This characterization gives a common generalization of all the positive and negative results on diophantine henselian valuation rings and diophantine valuation ideals in the literature.
Anscombe, Sylvy, Fehm, Arno
semanticscholar +7 more sources
Weighted Homology of Bi-Structures over Certain Discrete Valuation Rings
Mathematics, 2021 An RNA bi-structure is a pair of RNA secondary structures that are considered as arc-diagrams. We present a novel weighted homology theory for RNA bi-structures, which was obtained through the intersections of loops.
Andrei Bura, Qijun He, Christian Reidys
doaj +2 more sources
A Formalization of Complete Discrete Valuation Rings and Local Fields [PDF]
Certified Programs and Proofs, 2023 Local fields, and fields complete with respect to a discrete valuation, are essential objects in commutative algebra, with applications to number theory and algebraic geometry. We formalize in Lean the basic theory of discretely valued fields.
María Inés de Frutos-Fernández +1 more
semanticscholar +1 more source
A connectedness theorem for spaces of valuation rings [PDF]
Journal of Algebra, 2023 Let $F$ be a field, let $D$ be a local subring of $F$, and let Val$_F(D)$ be the space of valuation rings of $F$ that dominate $D$. We lift Zariski's connectedness theorem for fibers of a projective morphism to the Zariski-Riemann space of valuation ...
W. Heinzer +3 more
semanticscholar +1 more source
Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations [PDF]
Monatshefte für Mathematik (Print), 2022 Let V be a valuation ring of a global field K.
Victor Fadinger-Held +2 more
semanticscholar +1 more source
Essential finite generation of extensions of valuation rings [PDF]
Mathematische Nachrichten, 2021 Given a generically finite local extension of valuation rings V⊂W$V \subset W$ , the question of whether W is the localization of a finitely generated V‐algebra is significant for approaches to the problem of local uniformization of valuations using ...
Rankeya Datta
semanticscholar +1 more source
Characterizations of rings and modules by means of lattices [PDF]
, 1965 PhDIn this thesis we study the relationship between the lattice of submodules and the algebraic structure of a module. The key remark in our study will be the fact that the homomorphisms between two independent submadules of a module can be ...
Stephenson, W.
core +4 more sources
Valuation rings are derived splinters [PDF]
Mathematische Zeitschrift, 2020 We give three proofs that valuation rings are derived splinters: a geometric proof using absolute integral closure, a homological proof which reduces the problem to checking that valuation rings are splinters (which is done in the second author’s PhD ...
Benjamin Antieau, Rankeya Datta
semanticscholar +1 more source