GAP Manual: 5.1. IsRing

IsRing( domain )

IsRing returns true if the object domain is a ring record, representing a ring (see Ring Records), and false otherwise.

More precisely IsRing tests whether domain is a ring record (see Ring Records). So for example a matrix group may in fact be a ring, yet IsRing would return false. 

    gap> IsRing( Integers );
    true
    gap> IsRing( Rationals );
    false    # 'Rationals' is a field record not a ring record
    gap> IsRing( rec( isDomain := true, isRing := true ) );
    true    # it is possible to fool 'IsRing'
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