2020 Mathematics Subject Classification: Primary: 13A05 [MSN][ZBL]
For other meanings of the term 'Divisor' see the page Divisor (disambiguation)
A divisor of an integer is an integer which divides without remainder. In other words, a divisor of the integer is an integer such that, for a certain integer , the equality holds. A proper divisor or an aliquot divisor of is a natural number divisor of other than itself.
A divisor of a polynomial is a polynomial that divides without remainder (cf. Division).
More generally, in an arbitrary ring , a divisor of an element is an element such that for a certain .
If is a divisor of , one writes .
If divides and divides , then and are associates. If an element has the property that whenever , one of is an associate of , then is irreducible. For polynomials, see Irreducible polynomial; for integers, the traditional terminology is prime number.
References[edit]
- David Sharpe, Rings and Factorization Cambridge University Press (1987) ISBN 0-521-33718-6 Zbl 0674.13008