Results 21 to 30 of about 2,005,027 (257)
Implicit linear difference equations over a non-Archi-medean ring
Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2021 Over any field an implicit linear difference equation one can reduce to the usual explicit one, which has infinitely many solutions ~ one for each initial value.
Anna Goncharuk
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The Grothendieck–Serre conjecture over valuation rings [PDF]
Compositio Mathematica, 2020 In this article, we establish the Grothendieck–Serre conjecture over valuation rings: for a reductive group scheme $G$ over a valuation ring $V$ with fraction field $K$, a $G$-torsor over $V$ is trivial if it is trivial over $K$. This result is predicted
N. Guo
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An inductive approach to representations of general linear groups over compact discrete valuation rings [PDF]
Advances in Mathematics, 2020 In his seminal Lecture Notes in Mathematics published in 1981, Andrey Zelevinsky introduced a new family of Hopf algebras which he called {\em PSH-algebras}. These algebras were designed to capture the representation theory of the symmetric groups and of
Tyrone Crisp, E. Meir, U. Onn
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Some mixed matrix problems over several discrete valuation rings [PDF]
Journal of Applied Mathematics and Computational Mechanics, 2013 This article presents some results about several district valuation rings with a common skew field of fractions. They are obtained from the approximation theorem for discrete valuation rings. These results give the possibility to solve basic mixed matrix
Nadiya Gubareni
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, 1970 The theory of near-rings has arisen in a variety of ways. There is a natural desire to generalise the theory of rings and skew fields by relaxing some of their defining axioms.
Holcombe, William Michael Lloyd
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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
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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
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Trees and valuation rings [PDF]
Transactions of the American Mathematical Society, 2000 A subring B B of a division algebra
Brungs, Hans, Gräter, Joachim
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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 +1 more
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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
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