Results 11 to 20 of about 1,487,509 (274)

Characterizations of Pairs of Rings with Few Non-Dedekind Intermediary Rings

Journal of Mathematics, 2022
We determine the Dedekind domain pairs of rings; that is, pairs of rings R⊂S such that each intermediary ring in between R and S is a Dedekind domain. We also establish that if R⊂S is an extension of rings having only one non-Dedekind intermediary ring ...
Naseam Al-Kuleab, Noômen Jarboui
doaj   +1 more source

Grothendieck–Serre in the quasi-split unramified case

Forum of Mathematics, Pi, 2022
The Grothendieck–Serre conjecture predicts that every generically trivial torsor under a reductive group scheme G over a regular local ring R is trivial. We settle it in the case when G is quasi-split and R is unramified.
Kęstutis Česnavičius
doaj   +1 more source

Trees and valuation rings [PDF]

Transactions of the American Mathematical Society, 2000
A subring B B of a division algebra
Brungs, Hans, Gräter, Joachim
openaire   +3 more sources

Essentially finite generation of valuation rings in terms of classical invariants [PDF]

Mathematische Nachrichten, 2019
The main goal of this paper is to study some properties of an extension of valuations from classical invariants. More specifically, we consider a valued field (K,ν) and an extension ω of ν to a finite extension L of K.
S. Cutkosky, J. Novacoski
semanticscholar   +1 more source

On the Borderline of Fields and Hyperfields

Mathematics, 2023
The hyperfield came into being due to a mathematical necessity that appeared during the study of the valuation theory of the fields by M. Krasner, who also defined the hyperring, which is related to the hyperfield in the same way as the ring is related ...
Christos G. Massouros, Gerasimos G. Massouros   +1 more
doaj   +1 more source

Cramer's rule for implicit linear differential equations over a non-Archimedean ring

Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2022
We consider a linear nonhomogeneous $m$-th order differential equation in a ring of formal power series with coefficients from some field of characteristic zero.
A. Goncharuk
doaj   +1 more source

Ramification theory for degree p extensions of arbitrary valuation rings in mixed characteristic (0, p ) [PDF]

Journal of Algebra, 2017
We previously obtained a generalization and refinement of results about the ramification theory of Artin-Schreier extensions of discretely valued fields in characteristic $p$ with perfect residue fields to the case of fields with more general valuations ...
Vaidehee Thatte
semanticscholar   +1 more source

Gersten's injectivity for smooth algebras over valuation rings [PDF]

Advances in Mathematics
Gersten's injectivity conjecture for a functor $F$ of ``motivic type'', predicts that given a semilocal, ``non-singular'', integral domain $R$ with a fraction field $K$, the restriction morphism induces an injection of $F(R)$ inside $F(K)$.
Arnab Kundu
semanticscholar   +1 more source

Donovan’s conjecture, blocks with abelian defect groups and discrete valuation rings [PDF]

Mathematische Zeitschrift, 2018
We give a reduction to quasisimple groups for Donovan’s conjecture for blocks with abelian defect groups defined with respect to a suitable discrete valuation ring $${\mathcal {O}}$$ O . Consequences are that Donovan’s conjecture holds for $${\mathcal {O}
Charles W. Eaton, F. Eisele, M. Livesey
semanticscholar   +1 more source

On Valuation Rings

Communications in Algebra, 2010
In this paper we provide necessary and sufficient conditions for $ R=A\propto E $ to be a valuation ring where $E$ is a non-torsion or finitely generated $A-$module. Also, we investigate the $ (n,d) $ property of the valuation ring.
Kabbour, Mohammed, Mahdou, Najib
openaire   +2 more sources