scholarly journals Dagger completions and bornological torsion-freeness

2019 ◽  
Vol 70 (3) ◽  
pp. 1135-1156
Author(s):  
Ralf Meyer ◽  
Devarshi Mukherjee
Keyword(s):  
Spectral Radius ◽  
Valuation Ring ◽  
Discrete Valuation Ring ◽  
Torsion Freeness ◽  
Inheritance Properties

Abstract We define a dagger algebra as a bornological algebra over a discrete valuation ring with three properties that are typical of Monsky–Washnitzer algebras, namely, completeness, bornological torsion-freeness and a certain spectral radius condition. We study inheritance properties of the three properties that define a dagger algebra. We describe dagger completions of bornological algebras in general and compute some non-commutative examples.

scholarly journals Barrelled Linearly Topologized Modules Over a Discrete Valuation Ring

2020 ◽  
Vol 12 (1) ◽  
pp. 69
Author(s):  
Dinamérico P. Pombo Jr ◽  
Patricia Couto G. Mauro
Keyword(s):  
Valuation Ring ◽  
Discrete Valuation Ring ◽  
Continuous Linear ◽  
Steinhaus Theorem

In this paper barrelled linearly topologized modules over an arbitrary discrete valuation ring are introduced. A general form of the Banach-Steinhaus theorem for continuous linear mappings on barrelled linearly topologized modules is established and some consequences of it are derived.

The Reduction of an RG–Lattice Modulo pn

1990 ◽  
Vol 42 (2) ◽  
pp. 342-364 ◽  
Author(s):  
Peter Symonds
Keyword(s):  
Finite Group ◽  
Characteristic Zero ◽  
Valuation Ring ◽  
Discrete Valuation Ring ◽  
Prime Element ◽  
Class Field ◽  
Complete Discrete Valuation Ring ◽  
Projective Lattice ◽  
A Finite Group

We define the cover of an RG-module V to consist of an RG lattice Ṽ and a homomorphism π : Ṽ→ V such that π induces an isomorphism on Ext*RG(M, —) for any RG-lattice M. Here G is a finite group and, for simplicity in this introduction, R is a complete discrete valuation ring of characteristic zero with prime element p and perfect valuation class field. Let pn(G) be the highest power of p that divides |G| and, given an RG-lattice M, let pn(M) be the smallest power of p such that pn(M) idM : M→M factors through a projective lattice: n(M)≦n(G).

Polynomial index in discrete valuation rings

2019 ◽  
Vol 56 (2) ◽  
pp. 260-266
Author(s):  
Mohamed E. Charkani ◽  
Abdulaziz Deajim
Keyword(s):  
Lower Bound ◽  
Valuation Ring ◽  
Irreducible Polynomial ◽  
Discrete Valuation Ring ◽  
Field Extension ◽  
Integral Closure ◽  
Quotient Field ◽  
Discrete Valuation Rings ◽  
Valuation Rings ◽  
Adic Valuation

Abstract Let R be a discrete valuation ring, its nonzero prime ideal, P ∈R[X] a monic irreducible polynomial, and K the quotient field of R. We give in this paper a lower bound for the -adic valuation of the index of P over R in terms of the degrees of the monic irreducible factors of the reduction of P modulo . By localization, the same result holds true over Dedekind rings. As an important immediate application, when the lower bound is greater than zero, we conclude that no root of P generates a power basis for the integral closure of R in the field extension of K defined by P.

scholarly journals On the lifting of the Dade group

2019 ◽  
Vol 22 (3) ◽  
pp. 441-451
Author(s):  
Caroline Lassueur ◽  
Jacques Thévenaz
Keyword(s):  
Valuation Ring ◽  
Residue Field ◽  
Discrete Valuation Ring ◽  
Group Homomorphism ◽  
Complete Discrete Valuation Ring ◽  
Dade Group

Abstract For the group of endo-permutation modules of a finite p-group, there is a surjective reduction homomorphism from a complete discrete valuation ring of characteristic 0 to its residue field of characteristic p. We prove that this reduction map always has a section which is a group homomorphism.

scholarly journals Arithmetic 𝒟-modules on the unit disk. With an appendix by Shigeki Matsuda

2011 ◽  
Vol 148 (1) ◽  
pp. 227-268 ◽  
Author(s):  
Richard Crew
Keyword(s):  
Unit Disk ◽  
Valuation Ring ◽  
Discrete Valuation Ring ◽  
Mixed Characteristic ◽  
Complete Discrete Valuation Ring ◽  
Canonical Extensions

AbstractLet 𝒱 be a complete discrete valuation ring of mixed characteristic. We classify arithmetic 𝒟-modules on Spf(𝒱[[t]]) up to certain kind of ‘analytic isomorphism’. This result is used to construct canonical extensions (in the sense of Katz and Gabber) for objects of this category.

Extending Endo-monomial Modules

2013 ◽  
Vol 20 (01) ◽  
pp. 169-172
Author(s):  
Ziqun Lu ◽  
Jiping Zhang
Keyword(s):  
Finite Group ◽  
Valuation Ring ◽  
Residue Field ◽  
Discrete Valuation Ring ◽  
Characteristic P ◽  
Complete Discrete Valuation Ring ◽  
A Finite Group

Let G be a finite group with a normal Sylow p-subgroup P. Let [Formula: see text] be a complete discrete valuation ring with residue field F of characteristic p. Let M be an indecomposable endo-monomial [Formula: see text]-module. In this paper we prove that M extends to an [Formula: see text]-module if and only if M is G-stable. A similar and well-known version for endo-permutation modules is due to Dade.

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