associates (original) (raw)

Two elements in a ring with unity are associates or associated elements of each other if one can be obtained from the other by multiplying by some unit, that is, a and b are associates if there is a unit u such that a=b⁢u. Equivalently, one can say that two associates are divisible by each other.

Examples. In the ring ℤ of the rational integers, only opposite numbers ±n are associates. Among the polynomials, the associates of a polynomial are gotten by multiplying the polynomial by an element belonging to the coefficient ring in question (and being no zero divisor).