Ideals (ring theory)

Real radical

In algebra, the real radical of an ideal I in a polynomial ring with real coefficients is the largest ideal containing I with the same vanishing locus.It plays a similar role in real algebraic geometry that the radical of an ideal plays in algebraic geometry over an algebraically closed field.More specifically, the Nullstellensatz says that when I is an ideal in a polynomial ring with coefficients coming from an algebraically closed field, the radical of I is the set of polynomials vanishing on the vanishing locus of I. In real algebraic geometry, the Nullstellensatz fails as the real numbers are not algebraically closed. However, one can recover a similar theorem, the real Nullstellensatz, by using the real radical in place of the (ordinary) radical. (Wikipedia).

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Simplifying a radical expression to rational exponents

👉 Learn how to convert a radical to rational power. A radical is an expression having the root/radical symbol. The number outside the radical symbol (nth root) is called the index, the number/expression inside the radical symbol is called the radical. To convert a radical to a rational p

From playlist Numbers Raised to Fractional Exponents

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How to write a radical into a term with rational exponents

👉 Learn how to convert a radical to rational power. A radical is an expression having the root/radical symbol. The number outside the radical symbol (nth root) is called the index, the number/expression inside the radical symbol is called the radical. To convert a radical to a rational p

From playlist Numbers Raised to Fractional Exponents

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Converting a radical expression to a exponent with a rational power root

👉 Learn how to convert a radical to rational power. A radical is an expression having the root/radical symbol. The number outside the radical symbol (nth root) is called the index, the number/expression inside the radical symbol is called the radical. To convert a radical to a rational p

From playlist Numbers Raised to Fractional Exponents

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Learning how to rewrite an expression from radical form to a rational power

👉 Learn how to convert a radical to rational power. A radical is an expression having the root/radical symbol. The number outside the radical symbol (nth root) is called the index, the number/expression inside the radical symbol is called the radical. To convert a radical to a rational p

From playlist Numbers Raised to Fractional Exponents

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Using parenthesis to help convert a rational expression from radical form

👉 Learn how to convert a radical to rational power. A radical is an expression having the root/radical symbol. The number outside the radical symbol (nth root) is called the index, the number/expression inside the radical symbol is called the radical. To convert a radical to a rational p

From playlist Numbers Raised to Fractional Exponents

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How to rewrite an expression from a radical to a rational exponent root

👉 Learn how to convert a radical to rational power. A radical is an expression having the root/radical symbol. The number outside the radical symbol (nth root) is called the index, the number/expression inside the radical symbol is called the radical. To convert a radical to a rational p

From playlist Numbers Raised to Fractional Exponents

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Learn how to write an exponent with a rational power as a radical

👉 Learn how to convert a rational power to a radical. When the exponent of an expression is a fraction, we can evaluate/simplify the expression by converting the rational power into a radical where the denominator of the fractional exponent of the rational power becomes the index (nth root

From playlist Convert Fractional Exponents to Radicals

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Converting a rational exponent to radical form

👉 Learn how to convert a rational power to a radical. When the exponent of an expression is a fraction, we can evaluate/simplify the expression by converting the rational power into a radical where the denominator of the fractional exponent of the rational power becomes the index (nth root

From playlist Convert Fractional Exponents to Radicals

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How to rewrite the 4th root of a variable with a rational exponent

👉 Learn how to convert a radical to rational power. A radical is an expression having the root/radical symbol. The number outside the radical symbol (nth root) is called the index, the number/expression inside the radical symbol is called the radical. To convert a radical to a rational p

From playlist Numbers Raised to Fractional Exponents

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Nonlinear algebra, Lecture 5: "Nullstellensätze ", by Bernd Sturmfels

This is the fifth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences. Hilbert’s Nullstellensatz is a classical result from 1890, which offers a characterization of the set of all polynomials that vanish on a given v

From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra

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Algebraic Structures: Groups, Rings, and Fields

This video covers the definitions for some basic algebraic structures, including groups and rings. I give examples of each and discuss how to verify the properties for each type of structure.

From playlist Abstract Algebra

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Complex Numbers, Part 1

An introduction to Complex Numbers. First video in a short series, appropriate for Algebra 2 and up. This material is from the distance learning course by Derek Owens. Distance learning course are available at http://www.derekowens.com

From playlist Algebra 2 - Complex Numbers

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No More Extraneous Roots CONFUSION – Radical Equations

TabletClass Math: https://tcmathacademy.com/ How to solve radical equations and check for extraneous roots. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algeb

From playlist GED Prep Videos

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Let’s Solve The Radical Equation….Step-by-Step….

TabletClass Math: https://tcmathacademy.com/ Math help with solving radical equations and checking for extraneous roots or solutions. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Ma

From playlist Algebra

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Writing the domain of a rational function with the radical in the numerator

👉 Learn how to find the domain of rational functions with a radical numerator. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero and for radical functions, the value inside the radica

From playlist Domain of a function with a square root in the numerator

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Galois theory: Abel's theorem

This lecture is part of an online graduate course on Galois theory. We discuss Abel's theorem, that says a general quintic equation cannot be solved by radicals. We do this by showing that if a polynomial can be solved by radicals over a field of characteristic 0 then its roots lie in a s

From playlist Galois theory

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4. Stability

MIT Electronic Feedback Systems (1985) View the complete course: http://ocw.mit.edu/RES6-010S13 Instructor: James K. Roberge License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT Electronic Feedback Systems (1985)

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Learn how to rewrite an expression using the value i, 5 - root(-24)

👉 Learn how to simplify radical expressions. In this playlist we will explore simplifying radical expressions by prime factorization and rules of exponents. We will explore the square root, cube root as well as the fourth root of numbers and algebraic expressions with variables and expon

From playlist How to Simplify the Square Root of a Number

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How to write a term with a rational exponent in radical form

👉 Learn how to convert a rational power to a radical. When the exponent of an expression is a fraction, we can evaluate/simplify the expression by converting the rational power into a radical where the denominator of the fractional exponent of the rational power becomes the index (nth root

From playlist Convert Fractional Exponents to Radicals

Related pages

Radical of an ideal | Polynomial | Algebraically closed field | Coefficient | Real algebraic geometry | Ideal (ring theory) | Real number | Algebraic geometry | Algebra | Polynomial ring