Radical

Radical, from Late Latin radicalis "of roots" and from Latin radix "root", may refer to:

In chemistry:

• A radical (chemistry) is an atom, molecule, or ion, that is likely to take part in chemical reactions

In mathematics:

• Radical symbol (√), a symbol used to indicate the square root or nth root
• 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, in ring theory, a radical of a ring is an ideal of "bad" elements of the ring
• Radical of a module, in the theory of modules, the radical of a module is a component in the theory of structure and classification
• Jacobson radical, the Jacobson radical of a ring, R, consists of those elements in R that annihilate all simple right R-modules
• Nilradical of a ring, the nilradical of a commutative ring is a nilpotent ideal, which is as large as possible
• Nilradical of a Lie algebra, the nilradical of a Lie algebra is a nilpotent ideal, which is as large as possible
• Radical of an integer, in number theory, the radical of an integer is the product of the primes which divide that integer
• Left (or right) radical of a bilinear form, the subspace of all vectors left (or right) orthogonal to every vector.
• Radical of a Lie algebra, a concept in Lie theory

In medicine:

• Radical surgery, surgery carried out in extreme circumstances and/or with extensive treatment

In linguistics:

• In an inflected language such as English or Spanish, the radical verbs (also called 'radical-changing') are exceptions to the standard patterns of word change (e.g., to be is in most Indo European languages).
• Root (linguistics), also called a "radical", the form of a word after any prefixes and suffixes are removed
• Radical (Chinese character), part of a Chinese character under which it is indexed in a dictionary (also called bùshǒu 部首)
• Radical, one of the three consonants in a Semitic root
• Radical consonant, a consonant articulated with the root of the tongue

In politics:

• Political radicalism
• Radicalism (historical), the Radical Movement that began in late 18th century Britain and spread to continental Europe and Latin America in the 19th century
• Radical left, another term for the far left
• Radical right, another term for the far right
• Radical Whigs, influential early writers on Radicalism
• Radical Republicans, a member of an influential group of American politicians during the Civil War reconstruction
• Radical Party, one of a number of political parties around the world
• Radicals (UK), parliamentary progressives who were part of the nineteenth-century Liberal coalition
• Radicalization

In religion:

• Radical Reformation, an Anabaptist movement concurrent with the Protestant Reformation
• Radical Christianity
• Radical Islam
• Radical: Taking Back Your Faith from the American Dream, 2010 Christian book

In culture:

• Radical feminism, a current within feminism that focuses on patriarchy as a system of power
• Radical veganism, a radical interpretation of veganism, usually combined with anarchism
• Radical chic, a term coined by Tom Wolfe to describe the pretentious adoption of radical causes by celebrities, socialites, and high society

In architecture:

• Radical Baroque, an architectural style characterized by the curvature of walls and intersection of oval spaces

In music:

• Radical (mixtape), a mixtape by the alternative hip hop collective OFWGKTA
• "Radicals" (song), a song by Tyler, The Creator from his album Goblin
• Free Radicals (band), a jazz-funk musical group from Houston, Texas
• New Radicals, an American pop rock band from the 1990s
• Radical (album), Smack's fourth studio album, released in 1988

Brands, titles and proper names:

• Radical Sportscars, an English sports car maker
• Radical Entertainment, a video game developer based in Vancouver, Canada
• Free Radical Design, a video game developer based in Nottingham, England
• Free Radical Centre, a centre for free radical chemistry and biotechnology that was established in 2005