[GAP Forum] Misunderstanding about principle ideals of a semigroup
Mohammad Reza Sorouhesh
msorouhesh at gmail.com
Sun Mar 30 12:01:36 BST 2014
Dear Forum,
We know that what we call a J-Class in a finite semigroup is really a
principle ideal generated by an element of the semigroup. Here is a
finitely presented semigroup of order 8:
gap> f:=FreeSemigroup("a","b");;
a:=f.1;; b:=f.2;;
s:=f/[[a^3,a],[b^2*a,a*b],[(a*b)^2*b,b]];;
e:=Elements(s);
Now, lets the following code calls the two-sided ideal generated by e[1]:
> Elements(SemigroupIdealByGenerators(s,[e[1]]));
[ a, a^2*b, a^2, a*b, b*a, a*b*a, b*a*b, a*b*a*b ]
But by doing:
> GreensJClasses(s);
none of the Green J-Classes of semigroup "s" is equal to above set. Simply
asking why two below codes have different outputs? Or, I am mistaking about
a very simple fact which is clear?
Regards
M.R.Sorouhesh
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