scholarly journals Some Cases of Extensions of Twisted Group Schemes over a Discrete Valuation Ring

2000 ◽  
Vol 227 (2) ◽  
pp. 474-498
Author(s):  
Toshiaki Ohno
Keyword(s):  
Valuation Ring ◽  
Discrete Valuation Ring ◽  
Group Schemes ◽  
Twisted Group

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.

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