GAP Manual: 5.6. Quotient

Quotient( r, s )
Quotient( R, r, s )

In the first form Quotient returns the quotient of the two ring elements r and s in their default ring (see DefaultRing). In the second form Quotient returns the quotient of the two ring elements r and s in the ring R. It returns false if the quotient does not exist.

    gap> Quotient( 4, 2 );
    2
    gap> Quotient( Integers, 3, 2 );
    false 

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

The default function called this way is RingOps.Quotient, which just signals an error, because there is no generic method to compute the quotient of two ring elements. Thus special categories of rings must overlay this default function with other functions.