Results 31 to 40 of about 2,005,027 (257)
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
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
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Gersten's injectivity for smooth algebras over valuation rings [PDF]
Advances in MathematicsGersten'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
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Enumerating traceless matrices over compact discrete valuation rings [PDF]
Israel Journal of Mathematics, 2017 We enumerate traceless square matrices over finite quotients of compact discrete valuation rings by their image sizes. We express the associated rational generating functions in terms of statistics on symmetric and hyperoctahedral groups, viz.
A. Carnevale, Shai Shechter, C. Voll
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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
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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
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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 +2 more
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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.
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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
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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
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