Dear GAP forum,
Is it possible to obtain finite Galois Rings and their multiplicative group
of units in GAP?
Namely, factor rings of Z_{p^n}[x] by a basic irreducible polynomial over
Z_{p^n}.
I know how to build PolynomialRing but can't obtain factor rings by ideals.
This is an output of my GAP (4.6.3) session :
gap> T:=Integers mod 4;
(Integers mod 4)
gap> x:= Indeterminate( T, "x" );
x
gap> Pol:=x^4+x+1;
x^4+x+ZmodnZObj(1,4)
gap> R:=PolynomialRing( T );
<object>[x]
gap> Pol in R;
true
gap> I:=IdealByGenerators(R, [Pol]);
<two-sided ideal in <object>[x], (1 generators)>
gap> NaturalHomomorphismByIdeal( R, I );
Error, no method found! For debugging hints type ?Recovery from
NoMethodFound
Error, no 3rd choice method found for `NaturalHomomorphismByIdeal' on 2
arguments called from
<function "HANDLE_METHOD_NOT_FOUND">( <arguments> )
called from read-eval loop at line 32 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
NaturalHomomorphismByIdeal doesn't work even when T is a finite field of a
prime order (so in this case the corresponding factor ring should be also a
finite field).
Does anyone know how It can be calculated?
Best regards,
Staroletov Alexey
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