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Equations and Dot-Depth One By: Francine Blanchet
Equations and Dot-Depth One By: Francine Blanchet

The Division Theorem • Theorem Let n be a fixed integer ≥ 2. For
The Division Theorem • Theorem Let n be a fixed integer ≥ 2. For

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algebraic expression

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A PROPERTY OF SMALL GROUPS A connected group of Morley

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Agmon`s type estimates of exponential behavior of solutions of

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On the Equipollence of the Calculi Int and KM

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Every set has its divisor

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Exercises on binary quadratic forms

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A Construction of the Real Numbers - Math

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Mathematical Methods (CO-145)

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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.
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