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Rings

Algebraic structures generalizing integer arithmetic.

Ring structures

In mathematics, rings are algebraic structures consisting of a set equipped with two binary operations—typically addition and multiplication—that generalize the arithmetic properties of integers.

Pronunciation

/rɪŋ/

Etymology

The term 'ring' was introduced by David Hilbert in 1897, drawing an analogy to the integers.

Explain Like I’m 5

Rings are like regular numbers, but with extra rules that let you add, subtract, and multiply them, even if they aren't whole numbers.

Fun Facts

The set of integers is a classic example of a ring
Rings generalize the familiar arithmetic operations we use every day
Zero divisors can exist in rings, which doesn't happen with regular numbers

FAQ

What is a ring? A ring is an algebraic structure with addition and multiplication operations that satisfy certain properties
What are examples of rings? Integers, polynomials, and matrices are all examples of rings
Why are rings useful? Rings are used in abstract algebra, cryptography, and coding theory

Hypernyms — Broader Categories

Algebraic structure

Hyponyms — Specific Examples

Integral domain Field Commutative ring

Indexes

abstract structure mathematical concept

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