Simple Proof of a Fundamental Theorem of Field Theory

1959 ◽  
Vol 66 (9) ◽  
pp. 804 ◽  
Author(s):  
A. Kertesz
Keyword(s):  
Field Theory ◽  
Simple Proof ◽  
Fundamental Theorem

scholarly journals A SIMPLE PROOF OF THE FUNDAMENTAL THEOREM ABOUT ARVESON SYSTEMS

2006 ◽  
Vol 09 (02) ◽  
pp. 305-314 ◽  
Author(s):  
MICHAEL SKEIDE
Keyword(s):  
Hilbert Space ◽  
Simple Proof ◽  
Fundamental Theorem ◽  
Hilbert Module ◽  
Bounded Operators ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Product Systems ◽  
Dimensional Hilbert Space ◽  
The One

With every E0-semigroup (acting on the algebra of of bounded operators on a separable infinite-dimensional Hilbert space) there is an associated Arveson system. One of the most important results about Arveson systems is that every Arveson system is the one associated with an E0-semigroup. In these notes we give a new proof of this result that is considerably simpler than the existing ones and allows for a generalization to product systems of Hilbert module (to be published elsewhere).

scholarly journals Fundamental Theorems of Pure Mathematics & Absolute Geometry

2021 ◽  
Vol 4 (2) ◽  
Keyword(s):  
Field Theory ◽  
Number Theory ◽  
Fundamental Theorem ◽  
Absolute Geometry ◽  
Pure Mathematics ◽  
And Algebra ◽  
Fundamental Theorems

The superunified field theory consists of a row of discoveries in the realm of pure mathematics. It is two centuries ago that Karl Gauss unified higher arithmetic (number theory), algebra and geometry into what is called pure mathematics. The latter, however, still remains without its fundamental theorem despite that arithmetic and algebra, or even analysis, have their own.

scholarly journals Three Proofs that the Square Root of 2 Is Irrational

2021 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Field Theory ◽  
Simple Proof ◽  
Abstract Algebra ◽  
Background Information ◽  
Square Root ◽  
Clemson University ◽  
Short Article ◽  
Proof By Contradiction

This short article gives three proofs that the square root of 2 is irrational. The article is written in an expository tutorial format and the background information is provided in brief. The first proof is a simple proof by contradiction and the second and third proofs use field theory from abstract algebra. All three topics are developed and explained. For more details, please see this excellent course at Clemson University.

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