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Radical expression involving roots, also known as an nth root; Radical symbol (√), used to indicate the square root and other roots; Radical of an algebraic group, a concept in algebraic group theory; Radical of an ideal, an important concept in abstract algebra; Radical of a ring, an ideal of "bad" elements of a ring
Radical elimination can be viewed as the reverse of radical addition. In radical elimination, an unstable radical compound breaks down into a spin-paired molecule and a new radical compound. Shown below is an example of a radical elimination reaction, where a benzoyloxy radical breaks down into a phenyl radical and a carbon dioxide molecule. [7]
In mathematics, the radical symbol, radical sign, root symbol, or surd is a symbol for the square root or higher-order root of a number. The square root of a number x is written as x , {\displaystyle {\sqrt {x}},}
An unresolved root, especially one using the radical symbol, is sometimes referred to as a surd [2] or a radical. [3] Any expression containing a radical, whether it is a square root, a cube root, or a higher root, is called a radical expression , and if it contains no transcendental functions or transcendental numbers it is called an algebraic ...
"Radicalism" or "radical liberalism" was a political ideology in the 19th century United States aimed at increasing political and economic equality. The ideology was rooted in a belief in the power of the ordinary man, political equality, and the need to protect civil liberties.
The Oxford English Dictionary traces usage of 'radical' in a political context to 1783. [2] The Encyclopædia Britannica records the first political usage of 'radical' as ascribed to Charles James Fox, a British Whig Party parliamentarian who in 1797 proposed a 'radical reform' of the electoral system to provide universal manhood suffrage, thereby idiomatically establishing the term 'Radicals ...
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A radical ideal (or semiprime ideal) is an ideal that is equal to its radical. The radical of a primary ideal is a prime ideal . This concept is generalized to non-commutative rings in the semiprime ring article.