Results 21 to 30 of about 1,487,509 (274)
A principal ideal theorem for compact sets of rank one valuation rings [PDF]
, 2017 Let $F$ be a field, and let Zar$(F)$ be the space of valuation rings of $F$ with respect to the Zariski topology. We prove that if $X$ is a quasicompact set of rank one valuation rings in Zar$(F)$ whose maximal ideals do not intersect to $0$, then the ...
B. Olberding
semanticscholar +1 more source
Polyhedra and parameter spaces for matroids over valuation rings [PDF]
Advances in Mathematics, 2017 In this paper we address two of the major foundational questions in the theory of matroids over rings. First, we provide a cryptomorphic axiomatisation, by introducing an analogue of the base polytope for matroids.
Alex Fink, Luca Moci
semanticscholar +1 more source
Frobenius splitting of valuation rings and F-singularities of centers [PDF]
Algebra & Number Theory, 2017 Using a local monomialization result of Knaf and Kuhlmann, we prove that the valuation ring of an Abhyankar valuation of a function field over a perfect ground field of prime characteristic is Frobenius split.
Rankeya Datta
semanticscholar +1 more source
Valuations and rings of quotients [PDF]
Proceedings of the American Mathematical Society, 1974 Valuations on a commutative ring, as defined by Manis, are considered in the special case where the domain of the valuation mapping is a ring of quotients of a given ring R R
openaire +1 more source
The Completion of a Ring with a Valuation [PDF]
Proceedings of the American Mathematical Society, 1972 This paper proves three main results: the completion of a commutative ring with respect to a Manis valuation is an integral domain; a necessary and sufficient condition is given that the completion be a field; and the completion is a field when the valuation is Harrison and the value group is archimedean ordered.
openaire +1 more source
On the Structure of Affine Flat Group Schemes Over Discrete Valuation Rings, II [PDF]
International mathematics research notices, 2017 In the first part of this work [ 12], we studied affine group schemes over a discrete valuation ring (DVR) by means of Neron blowups. We also showed how to apply these findings to throw light on the group schemes coming from Tannakian categories of ...
N. D. Duong, P. H. Hai, J. Santos
semanticscholar +1 more source
Filtrations and valuations on rings [PDF]
Bulletin of the Australian Mathematical Society, 1971 This thesis was scanned from the print manuscript for digital preservation and is copyright the author. Researchers can access this thesis by asking their local university, institution or public library to make a request on their behalf. Monash staff and postgraduate students can use the link in the References field.
openaire +5 more sources
Rings all of whose additive group endomorphisms are left multiplications
International Journal of Mathematics and Mathematical Sciences, 1984 Motivated by Cauchy's functional equation f(x+y)=f(x)+f(y), we study in §1 special rings, namely, rings for which every endomorphism f of their additive group is of the form f(x)≡ax. In §2 we generalize to R algebras (R a fixed commutative ring) and give
Michael I. Rosen, Oved shisha
doaj +1 more source
$G$-valuations and $G$-valuation rings
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
Illinois Journal of Mathematics, 2018 Let $(R, \mathfrak{m})$ be a complete discrete valuation ring with the finite residue field $R/\mathfrak{m} = \mathbb{F}_{q}$. Given a monic polynomial $P(t) \in R[t]$ whose reduction modulo $\mathfrak{m}$ gives an irreducible polynomial $\bar{P}(t) \in \
Gilyoung Cheong, Yifeng Huang
semanticscholar +1 more source