TENSOR PRODUCTS II 1. Introduction Continuing our study of
TENSOR PRODUCTS II 1. Introduction Continuing our study of

AN ALTERNATIVE CONSTRUCTION TO THE TRANSITIVE
AN ALTERNATIVE CONSTRUCTION TO THE TRANSITIVE

C3.1 Algebra and functions 1
C3.1 Algebra and functions 1

Some applications of the ultrafilter topology on spaces of valuation
Some applications of the ultrafilter topology on spaces of valuation

On Zero Semimodules of Systems over Semirings
On Zero Semimodules of Systems over Semirings

Fleury`s spanning dimension and chain conditions on non
Fleury`s spanning dimension and chain conditions on non

... We wsay that L is decomposable if there exist complements different from 0 and 1. An element a ∈ L shall be called decomposable if [0, a] is decomposable. Note that in case of L = L(M ), a submodule A of M is a complement in L(M ) if and only if it is a direct summand of M . A pseudo-complement of a ...
- Te Kura
- Te Kura

Some Complexity Results on Fuzzy Description Logics
Some Complexity Results on Fuzzy Description Logics

New finding of number theory By Liu Ran Contents 1
New finding of number theory By Liu Ran Contents 1

... In 32 bit computer, the biggest number is 2^32 = 4294967296. Any number is more than 4294967296 recorded as 4294967296+. Similarly, In 64 bit computer, the biggest number is 2^64 = 18446744073709551616. Any number being bigger than 2^64 is record as one number 2^64+. The natural number is from 1 to ...
Representation theory and applications in classical quantum
Representation theory and applications in classical quantum

Problems in the classification theory of non-associative
Problems in the classification theory of non-associative

Square Roots and Cube Roots
Square Roots and Cube Roots

Elementary Number Theory, A Computational Approach
Elementary Number Theory, A Computational Approach

On computable numbers, w - Department of Mathematics
On computable numbers, w - Department of Mathematics

Introduction to Exponents and Logarithms
Introduction to Exponents and Logarithms

Quaternions - Geometrical Anatomy
Quaternions - Geometrical Anatomy

arXiv:math/0510054v2 [math.HO] 17 Aug 2006
arXiv:math/0510054v2 [math.HO] 17 Aug 2006

FILTERED MODULES WITH COEFFICIENTS 1. Introduction Let E
FILTERED MODULES WITH COEFFICIENTS 1. Introduction Let E

... is coprime to the conductor of , then by work of Faltings the associated local Galois representation ρf |Gp : Gp → GL2 (E) is known to be semi-stable [Maz94, §12]. The associated filtered module Dst (ρf |Gp ) is as above with α = pap (see [Bre01, pp. 31-32], where the normalizations are slightly di ...
Acta Acad. Paed. Agriensis, Sectio Mathematicae 27 (2000) 25–38
Acta Acad. Paed. Agriensis, Sectio Mathematicae 27 (2000) 25–38

Lectures on Sieve Methods - School of Mathematics, TIFR
Lectures on Sieve Methods - School of Mathematics, TIFR

Semirings Modeling Confidence and Uncertainty in
Semirings Modeling Confidence and Uncertainty in

Basic Arithmetic Geometry Lucien Szpiro
Basic Arithmetic Geometry Lucien Szpiro

A Lefschetz hyperplane theorem with an assigned base point
A Lefschetz hyperplane theorem with an assigned base point

Notes on Discrete Mathematics CS 202: Fall 2013 James Aspnes 2014-10-24 21:23
Notes on Discrete Mathematics CS 202: Fall 2013 James Aspnes 2014-10-24 21:23

GROUP-THEORETIC AND TOPOLOGICAL INVARIANTS OF
GROUP-THEORETIC AND TOPOLOGICAL INVARIANTS OF

Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero.Equivalently (by definition), the theorem states that the field of complex numbers is algebraically closed.The theorem is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n roots. The equivalence of the two statements can be proven through the use of successive polynomial division.In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use the completeness of the reals (or some other equivalent formulation of completeness), which is not an algebraic concept. Additionally, it is not fundamental for modern algebra; its name was given at a time when the study of algebra was mainly concerned with the solutions of polynomial equations with real or complex coefficients.