radical

(historical, 19th-century Britain) A member of the most progressive wing of the Liberal Party; someone favouring social reform (but generally stopping short of socialism).

(historical, early 20th-century France) A member of an influential, centrist political party favouring moderate social reform, a republican constitution, and secular politics.

A person with radical opinions.

(arithmetic) A root (of a number or quantity).

(linguistics) In logographic writing systems such as the Chinese writing system, the portion of a character (if any) that provides an indication of its meaning, as opposed to phonetic.

(linguistics) In Celtic languages, refers to the basic, underlying form of an initial consonant which can be further mutated under the Celtic initial consonant mutations.

(linguistics) In Semitic languages, any one of the set of consonants (typically three) that make up a root.

(chemistry) A group of atoms, joined by covalent bonds, that take part in reactions as a single unit.

(organic chemistry) A free radical.

(algebra, commutative algebra, ring theory, of an ideal) Given an ideal I in a commutative ring R, another ideal, denoted Rad(I) or √, such that an element x ∈ R is in Rad(I) if, for some positive integer n, xⁿ ∈ I; equivalently, the intersection of all prime ideals containing I.

(algebra, ring theory, of a ring) Given a ring R, an ideal containing elements of R that share a property considered, in some sense, "not good".

(algebra, ring theory, of a module) The intersection of maximal submodules of a given module.

(number theory) The product of the distinct prime factors of a given positive integer.