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composite number
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composite number

Also known as: nonprime number

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arithmetic

  • A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”
    In arithmetic: Fundamental theory

    …1, then c is called composite. A positive integer neither 1 nor composite is called a prime number. Thus, 2, 3, 5, 7, 11, 13, 17, 19, … are prime numbers. The ancient Greek mathematician Euclid proved in his Elements (c. 300 bc) that there are infinitely many prime numbers.

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factors

  • In factor

    …than two factors is termed composite. The prime factors of a number or an algebraic expression are those factors which are prime. By the fundamental theorem of arithmetic, except for the order in which the prime factors are written, every whole number larger than 1 can be uniquely expressed as…

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ring
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ring

mathematics
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ring, in mathematics, a set having an addition that must be commutative (a + b = b + a for any a, b) and associative [a + (b + c) = (a + b) + c for any a, b, c], and a multiplication that must be associative [a(bc) = (ab)c for any a, b, c]. There must also be a zero (which functions as an identity element for addition), negatives of all elements (so that adding a number and its negative produces the ring’s zero element), and two distributive laws relating addition and multiplication [a(b + c) = ab + ac and (a + b)c = ac + bc for any a, b, c]. A commutative ring is a ring in which multiplication is commutative—that is, in which ab = ba for any a, b.

The simplest example of a ring is the collection of integers (…, −3, −2, −1, 0, 1, 2, 3, …) together with the ordinary operations of addition and multiplication.

This article was most recently revised and updated by William L. Hosch.
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