On an isotropy criterion for quadratic forms over function fields of curves over non-dyadic complete discrete valuation rings

2016 ◽  
Vol 108 ◽  
pp. 95-103
Author(s):  
David Grimm
Keyword(s):  
Quadratic Forms ◽  
Function Fields ◽  
Discrete Valuation Rings ◽  
Valuation Rings

Witts Theorem for Quadratic Forms Over Non-Dyadic Discrete Valuation Rings

1977 ◽  
Vol 29 (5) ◽  
pp. 928-936
Author(s):  
David Mordecai Cohen
Keyword(s):  
Bilinear Form ◽  
Maximal Ideal ◽  
Quadratic Forms ◽  
Valuation Ring ◽  
Discrete Valuation Ring ◽  
Symmetric Bilinear Form ◽  
Finitely Generated ◽  
Discrete Valuation Rings ◽  
Valuation Rings ◽  
Group Of Isometries

Let R be a discrete valuation ring, with maximal ideal pR, such that ½ ϵ R. Let L be a finitely generated R-module and B : L × L → R a non-degenerate symmetric bilinear form. The module L is called a quadratic module. For notational convenience we shall write xy = B(x, y). Let O(L) be the group of isometries, i.e. all R-linear isomorphisms φ : L → L such that B((φ(x), (φ(y)) = B(x, y).

scholarly journals Pencils of Quadratic Forms and Hyperelliptic Function Fields

2000 ◽  
Vol 227 (2) ◽  
pp. 532-548
Author(s):  
David B. Leep ◽  
Laura Mann Schueller
Keyword(s):  
Quadratic Forms ◽  
Function Fields ◽  
Hyperelliptic Function

scholarly journals On cuspidal representations of general linear groups over discrete valuation rings

2010 ◽  
Vol 175 (1) ◽  
pp. 391-420 ◽  
Author(s):  
Anne-Marie Aubert ◽  
Uri Onn ◽  
Amritanshu Prasad ◽  
Alexander Stasinski
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
General Linear Groups ◽  
Discrete Valuation Rings ◽  
Valuation Rings ◽  
Cuspidal Representations

Algorithms for quadratic forms over real function fields

2016 ◽  
Vol 108 ◽  
pp. 133-141
Author(s):  
Konrad Jałowiecki ◽  
Przemysław Koprowski
Keyword(s):  
Real Function ◽  
Quadratic Forms ◽  
Function Fields

Right Invariant Right Hereditary Rings

1974 ◽  
Vol 26 (5) ◽  
pp. 1186-1191 ◽  
Author(s):  
H. H. Brungs
Keyword(s):  
Principal Ideal ◽  
Prime Ideals ◽  
Maximal Orders ◽  
Discrete Valuation Rings ◽  
Valuation Rings ◽  
Dedekind Domains ◽  
Left Order ◽  
Principal Ideal Domains

Let R be a right hereditary domain in which all right ideals are two-sided (i.e., R is right invariant). We show that R is the intersection of generalized discrete valuation rings and that every right ideal is the product of prime ideals. This class of rings seems comparable with (and contains) the class of commutative Dedekind domains, but the rings considered here are in general not maximal orders and not Dedekind rings in the terminology of Robson [9]. The left order of a right ideal of such a ring is a ring of the same kind and the class contains right principal ideal domains in which the maximal right ideals are two-sided [6].

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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