Characterizations of simple A-algebras in terms of étale homomorphisms; invariance of the property of being a simple algebra under composition and change of base

1982 ◽  
pp. 89-102
Author(s):  
Richard Sot
Keyword(s):  
Simple Algebra

The Simple Algebra of Surplus in Open, Private Values Auctions

2017 ◽  
Author(s):  
Luke Froeb ◽  
Vlad Mares ◽  
Steven Tschantz
Keyword(s):  
Simple Algebra ◽  
Private Values

scholarly journals A simple algebra system

1968 ◽  
Vol 11 (3) ◽  
pp. 293-298 ◽  
Author(s):  
D. Barton
Keyword(s):  
Simple Algebra

scholarly journals Motivic decomposition of compactifications of certain group varieties

2018 ◽  
Vol 2018 (745) ◽  
pp. 41-58
Author(s):  
Nikita A. Karpenko ◽  
Alexander S. Merkurjev
Keyword(s):  
Central Simple Algebra ◽  
Simple Algebra ◽  
Chow Ring ◽  
Prime Degree ◽  
Central Simple

Abstract Let D be a central simple algebra of prime degree over a field and let E be an {\operatorname{\mathbf{SL}}_{1}(D)} -torsor. We determine the complete motivic decomposition of certain compactifications of E. We also compute the Chow ring of E.

Isotropy of orthogonal involutions in characteristic two

2018 ◽  
Vol 17 (12) ◽  
pp. 1850240 ◽  
Author(s):  
A.-H. Nokhodkar
Keyword(s):  
Quadratic Form ◽  
Central Simple Algebra ◽  
Simple Algebra ◽  
Characteristic Two ◽  
Central Simple ◽  
The Given

A totally singular quadratic form is associated to any central simple algebra with orthogonal involution in characteristic two. It is shown that the given involution is isotropic if and only if its corresponding quadratic form is isotropic.

scholarly journals Control Flow Treatment in a Simple: Semantics-Directed Compiler Generator

1981 ◽  
Vol 10 (137) ◽  
Author(s):  
Neil D. Jones ◽  
Henning Christiansen
Keyword(s):  
Simple Algebra ◽  
Control Flow ◽  
Program Execution ◽  
Correctness Proofs ◽  
Compiler Generation ◽  
Source Program ◽  
Target Program ◽  
Definition Of ◽  
Flow Treatment ◽  
Semantic Definition

<p>A simple algebra-based algorithm for compiler generation is described. Its input is a semantic definition of a programming language, and its output is a ''compiling semantics'' which maps each source program into a sequence of compile-time actions whose net effect on execution is the production of a semantically equivalent target program. The method does not require individual compiler correctness proofs or the construction of specialized target algebras.</p><p>Source program execution is assumed to proceed by performing a series of elementary actions on a runtime state. A semantic algebra is introduced to represent and manipulate possible execution sequences. A source semantic definition has two parts: A set of semantic equations mapping source programs into terms of the algebra, and an interpretation which gives concrete definitions of the state and the elementary actions on it.</p>

Simple Algebras Over Rational Function Fields

1979 ◽  
Vol 31 (4) ◽  
pp. 831-835 ◽  
Author(s):  
T. Nyman ◽  
G. Whaples
Keyword(s):  
Rational Function ◽  
Number Field ◽  
Matrix Algebra ◽  
Function Fields ◽  
Simple Algebra ◽  
Noether Theorem ◽  
Full Matrix ◽  
Full Matrix Algebra ◽  
Rank One ◽  
Simple Algebras

The well-known Hasse-Brauer-Noether theorem states that a simple algebra with center a number field k splits over k (i.e., is a full matrix algebra) if and only if it splits over the completion of k at every rank one valuation of k. It is natural to ask whether this principle can be extended to a broader class of fields. In particular, we prove here the following extension.

scholarly journals Splitting of Algebras by Function Fields of One Variable

1966 ◽  
Vol 27 (2) ◽  
pp. 625-642 ◽  
Author(s):  
Peter Roquette
Keyword(s):  
Tensor Product ◽  
Function Fields ◽  
Central Simple Algebra ◽  
Simple Algebra ◽  
Field Extension ◽  
Brauer Group ◽  
Central Simple Algebras ◽  
Natural Mapping ◽  
Simple Algebras ◽  
Central Simple

Let K be a field and (K) the Brauer group of K. It consists of the similarity classes of finite central simple algebras over K. For any field extension F/K there is a natural mapping (K) → (F) which is obtained by assigning to each central simple algebra A/K the tensor product which is a central simple algebra over F. The kernel of this map is the relative Brauer group (F/K), consisting of those A ∈(K) which are split by F.

INVARIANT EIGEN-OPERATOR METHOD OF DERIVING ENERGY-LEVEL GAP FOR NONCOMMUTATIVE QUANTUM MECHANICS

2005 ◽  
Vol 20 (09) ◽  
pp. 691-698 ◽  
Author(s):  
SI-CONG JING ◽  
HONG-YI FAN
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Operator Method ◽  
Simple Algebra ◽  
New Method ◽  
Noncommutative Quantum Mechanics ◽  
Noncommutative Quantum

We propose a new method to derive energy-level gap for Hamiltonians in the context of noncommutative quantum mechanics (NCQM). This method relies on finding invariant eigen-operators whose commutators with Hamiltonian are still the operators themselves but with some eigenvalue-like coefficients, which correspond to the energy-level gaps of the systems. Based on this method, only after some simple algebra, we derive the energy-level gaps for several important systems in NCQM, and most of these results have not been reported in literature so far.

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