[GAP Forum] question about Rees Matrix Semigroups

[Joao Araujo]

Let s be the full transformation semigroup on 4 elements:

t:=Transformation([1,2,3,3]);;
s:=Semigroup(Transformation([2,1,3,4]),Transformation([2,3,4,1]),t);;

Now we ask GAP to give us the Rees Zero Matrix Semigroup associated to the
D-class of t:

gap> ld:=GreensDClassOfElement(s,t);;
gap> rs:=AssociatedReesMatrixSemigroupOfDClass(ld);
Rees Zero Matrix Semigroup over Monoid( [ (1,2)(3,4)(5,6), (),
(1,5,4)(2,3,6), (1,6)(2,4)(3,5), (1,3)(2,5)(4,6),
  (1,4,5)(2,6,3), 0 ], ... )

Since the semigroup  s is regular, every D-class is regular and hence
there exists at least one non-zero entry in each row and in each column
in the Sandwich Matrix of rs.

However, when we ask GAP to give the associated matrix we get:

gap> SandwichMatrixOfReesZeroMatrixSemigroup(rs);
[ [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0 ], [ 0,
0, 0, 0, 0, 0 ] ]

If this was correct, then, in particular, the D-class of
t would have no idempotents (and hence t would be irregular).

I would be very grateful if someone could tell me what I am doing wrong.

Joao