GAP Manual: 5.15. Associates

Associates( r )
Associates( R, r )

In the first form Associates returns the set of associates of the ring element r in its default ring (see DefaultRing). In the second form Associates returns the set of associates of r in the ring R.

Two elements r and s of a ring R are called associate if there is a unit u of R such that r u = s.

    gap> Associates( Integers, 17 );
    [ -17, 17 ] 

Associates calls R.operations.Associates( R, r ) and returns the value.

The default function called this way is RingOps.Associates, which multiplies the set of units of R with the element r, and returns the set of those elements. Special categories of rings overlay this default function with more efficient functions.