Background for radicals

radicals

/ˈrædɪkəlz/

Illustration radicals - Image 1

noun

(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).

Examples :

"The radicals in the student council advocated for changes to the school's dress code. "

politics government history society

Illustration radicals - Image 1

noun

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

Examples :

"The radicals, a prominent political group in early 20th-century France, advocated for gradual changes to the education system. "

politics government history nation

Illustration radicals - Image 1

noun

A person with radical opinions.

Examples :

"The radicals in the student group proposed abolishing all homework, a much more extreme idea than simply reducing the workload. "

politics person attitude philosophy

Illustration radicals - Image 1

noun

A root (of a number or quantity).

Examples :

"In math class, we learned how to simplify radicals like the square root of 9. "

Illustration radicals - Image 1

noun

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.

Examples :

"When learning Chinese characters, understanding the radicals can help you guess the general meaning of a new word, even if you don't know its pronunciation. "

language linguistics writing character

Illustration radicals - Image 1

noun

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

Examples :

"In Arabic class, we learned that the three radicals k-t-b form the root meaning "write," and are used to build related words like "book" and "writer." "

language linguistics

Illustration radicals - Image 1

noun

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

Examples :

"In organic chemistry, radicals like methyl (CH3) or ethyl (CH2CH3) can detach from larger molecules and react with other substances to form new compounds. "

chemistry biology biochemistry

Illustration radicals - Image 1

noun

A free radical.

Examples :

"Example Sentence: "Antioxidants in fruits and vegetables help protect our bodies from damage caused by radicals." "

chemistry medicine biochemistry biology

Illustration radicals - Image 1

noun

(commutative algebra, of an ideal) Given an ideal I in a commutative ring R, another ideal, denoted Rad(I) or \sqrt{I}, 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.

Examples :

"In abstract algebra, understanding the relationship between ideals and their radicals is crucial for simplifying ring structures, much like simplifying fractions helps in basic arithmetic. "

math logic abstract

Illustration radicals - Image 1

noun

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

Examples :

"In abstract algebra, mathematicians study radicals of a ring to understand which elements might cause problems in calculations or analysis within that ring's structure. "

Illustration radicals - Image 1

noun

(of a module) The intersection of maximal submodules of a given module.

Examples :

"The radicals of the student council's fundraising committee are the shared interests of all the most powerful subgroups within the committee. "

Illustration radicals - Image 1

noun

The product of the distinct prime factors of a given positive integer.

Examples :

"In number theory problems, finding the radicals of integers helps simplify complex calculations. "